Final Exam Chapters 22-31 Flashcards
What is the difference between a conductor and an insulator?
Conductor- Usually metal, has 0 electric field, has free charges
Insulator- Usually non metal, has an electric field, has NO free charges
What does Coulomb’s law state?
Where
F= ma (mass x acceleration)
Q and q= Charges
r= Distance between the two charges
k= 8.99 x 10^9 (N x m^2/C^2)
The attractive force between the point charges 8.44E-6C and Q has a magnitude of 0.975N when the separation between the charges is 1.31m Find the sign and magnitude of the charge Q.
Q= 2.2E-5
Given that Q1= +12uC and d= 0.16m, find the direction and magnitude of the net electrostatic force exerted on the point charge q1
F1= F(1,2) + F(1,3)
F1= [k(+q)(2q) / (d^2)] + [k(+q)(3q) / 2(d^2)]
F1= [8.99E9(1 x 12E-6)(-2 x 12E-6) / (0.16^2)] + [8.99E9(1x 12E-6)(3x 12E-6) / (2 x0.16^2)]
F1= -101.13 + 37.89
F1= 63.24 (Would be negative to specify direction)
Suppose that a charge q2 can be moved left or right along the line connecting the charges q1 and q3. Given that q= +12uC, find the distance from q1 where q2 experiences a net electrostatic force of 0. The charges q1 and q3 are separated by a fixed distance of 0.32m.
Distance between 1 and 2= ? (X)
Distance between 1 and 3= (.32m-X)
F2= F(2,1) + F(2,3) BUT where F2=0
0= [k(-2q)(1q) / x^2] + [k(-2q)(3q) / (0.32m-x)^2]
- [k(-2q)(1q) / x^2] = [k(-2q)(3q) / (0.32m-x)^2]
(k’s and -2q’s cancel eachother out)
- [(1q)(0.32m-x)^2] = [(3q)(x^2)] > Do 3q/q= 3 and take square root
- (0.32m-x) = sqrt3(x)
x= (0.32m)/ 1 +- sqrt 3
x= 0.12 and -0.45
Find the orbital radius for which the kinetic energy of the electron in example 19-1 is 1.51 ev.
*1ev = 1 electron volt = 1.6E-19
* F electrical = F centripetal
[k(q1)(q2)/r^2] = ma (centripetal) is equivalent to…
[k(e)^2/r^2] = m (v^2/r) > e is for electron
V^2 = k(e^2)/ (r)(m)
Kinetic energy= (1/2)(m)(v^2)
V^2= (K)(2)/(m) > Set v^2’s equal to each other
k(e^2)/ (r)(m) = (K)(2)/(m)
Where r= k(e^2)/ 2K
r= (8.99E9)(1.6E-19C^2)/ 2(1.51ev)(1.60E-19)
r= 4.76E-10
Four point charges are located at the corners of a square with sides of length a. Two of the charges are +q and two are -q. Find the magnitude and direction of the net electric force exerted on a charge +Q, located t the center of the square, for each of the following 2 arrangements of charge; the charges alternate in sign +q,-q,+q,-q as you go around the square; the two positive charges are on the top corners, and the two negative charges are on the bottom corners.
- The first box has a F(net) of zero because the charges cancel out
- F(net)= 2F(x) + 2F(y) where a= Length
F(net)= 2[KqQ/ (a/sqrt2)^2] x sin(45) + 2[KqQ/ (a/sqrt2)^2] x sin(45)
F(net)= [-4(sqrt2)kqQ/ a^2]
What is the equation when charge Q is distributed over a sphere?
For point charges, each of magnitude q are located at the corners of a square with sides of length a. Two of the chargess are +q and two are -q. The charges are alternate in sign as you go around the square. The top 2 corners of the square have positive charges (-q,+q). In which case will the electric field at the center of the square have the greatest magnitude? Calculate the electric field at the center of the square for each of these 2 cases.
E= [kq/(1/2)(a^2)]
E1x + E2x + E3x + E4x= [kq/(1/2r^2) 1/sqrt2 +-1/sqrt2 + 1/sqrt2 +-1/sqrt2 = 0
E1y + E2y + E3xy+ E4y= -1/sqrt2 - 1/sqrt2 - 1/sqrt2 - 1/sqrt2 = [-4sqrt2(k)(q)/(r)^2]
The electric field lines surrounding 3 choices are shown. The center charge is q2= -10uC. What are the signs of q1 and q3? Find q3.
- Charges q1 and q3 must be positive
- The charge q1 has 8 lines leaving it, but q2 has 16 lines entering it. Because 8 is half of 16, and since the number of lines entering or leaving a charge is proportional to the magnitude of the charge, the magnitude of q1, is one-half of q2, or 5uC.
- By the reasoning of part b, the magnitude of q3 is 5uC
A surface encloses the charges q1= 3.2uC, q2= 6.9uC, and q3= -4.1uC. Find the electric flux through this surface.
6.8E-12 Nm^2/C
What is the equation for electric flux?
The cell membrane of a typical nerve cell consists of an inner and an outter wall separated by a distance of 0.10um. The electric fields within the cell membrane is 7.5E5. Approximating the cell membrane as a parallel-plate capacitator, determine the magnitude of the charge density on an inner and outer cell walls
A uniform electric field of magnitude 4.1E5 N/C points in the positive x-direction. Find the change in electric potential energy of a 4.5uC charge as it moves from the origin to the points (0,6m) (6m,0) (6m,6m)
What is the difference between electrical potential energy and electrical potential
An electrical plate capacitor has plates separated by 0.00075m. If the electric field between the plates has a magnitude of a.) 1.2E5 V/m or b.) 2.4E4 N/c, what is the potential difference between the plates?
A typical 12V car battery can deliver 7.5E5C of charge. If the energy supplied by the battery could be converted entirely to KE, what speed would give to a 1400kg car initially at rest?
The electrons in a TV picture tube are accelerated from rest through a potential difference of 25,000V. What is the speed of the electrons after they have been accelerated by this potential difference?
A proton has an initial speed of 4E5 m/s. a.) What potential difference is required to bring the proton to rest? b.) What potential difference is required to reduce the initial speed of the proton by a factor of 2? c.) What potential difference is required to reduce the initial kinetic energy of the proton by a factor of 2?
The hydrogen atom consists of one electron and one proton. In the Bohr model of the hydrogen atom, the electron orbits the proton in a circular orbit of radius 0.529E10 m. What is the electric potential due to the proton at the electrons orbit?
a.) Find the electric potential at point P in the figure. uppose the 3 charges shown are held in place. A fourth charge, with a charge of 6.11uC and a mass of 0.00471kg is released from rest at point p. b.) What is the speed of the fourth charge when it has moved infinitly far away from the other 3 charges?
A 0.40uF capacitor is connected to a 9v battery. How much charge is on each plate of the capacitor?
To operate a given flash lamp requires a charge of 32uC. What capacitance is needed to store this much charge in a capacitaor with a potential difference between its plates of 9V.
A parallel-plate capacitor has plates with an area of 0.012m^2 and a separation of 0.00088m. The space between the plates is filled with a dielectric constant is 2. What is the potential difference between the plates when the charge on the capacitor plates is 4.7uC? Will your answer to part a increase, decrease, or stay the same if the dielectric constant is increased? Explain. Calculate the potential difference for the case where the dielectric constant is 4.
In the Bohr model of the hydrogen atoms, what is the smallest amount of work that must be done on the electron to move it from its circular orbit, with a radius of 0.529E-10m, to an infinite distance from the proton? This value is referred to as the ionization energy of hydrogen.
How much work is required to bring 3 protons, initially infinitly far apart, to a configuration where each proton is 1.5E-15 m from the other two?
Many cells in the body have a cell membrane whose inner and outer surfaces carry opposite charges, just like the plates of a parallel-plate capacitor. Suppose a typical cell membranehas a thickness of 8.1E-9 m, and its inner and outer surfaces carry charge densities of 0.58E-3 C/m^2 and +5.8E-3 c/m^2, respectively. In addition, assume that the material in the cell has a di electric constant of 5.5. Find the direction and magnitude of the electric field within the cell membrane. Calculate the potential difference between the inner and outer walls of the membrane, and indicate which wall of the membrane has the higher potential
A flashlight bulb carries a current of 0.18A for 78 sec. How much charge flows through the bulb in this time? How many electrons?
A bird lands on a bore copper wire cayying a current of 32A. The wire is 8 gauge, which means that its cross-sectional area is 0.0013m^2. Find the difference in potential between the birds feet, assuming they are separated by a distance of 0.06m. Will your answer to part a.) increase or decrease if the separation between the birds feet increases? Explain.
A typical cel membrane is 8nm thick and has an electrical resitivity of 1.3E7 nxm. If the potential difference between the inner and outer surfaces of a cell membrane is 0.075v, how much current flows through a square area of membrane 1um on a side? Suppose the thickness of their membrane is doubled.
It costs 2.6 cents to charge a car batter of a voltage of 12V and a current of 15A for 120 minutes. What is the cost of electrical energy per kilawatt/hour of this location?
Suppose point A is grounded V=0. Find the potential at points B and C.
The tungsten filament of a lightbulb has a resisitence of 0.07 mu. If the filament is 0.27m long, what is its diameter?
Find the power dissapated in a 25mu electric heater connected to a 120-v outet.
Find the equivalent resistence between points A and B for the group of resistors shown.
What is the minimum number of 65mu resistors that must be connected in parallel to produce an equivalent resistance of 11mu or less?
Suppose A is grounded (V=0). Find the potential at points B and C.
An electron moves at right angles to a magnetic field of 0.18T. What is its speed if the force exerted on it is 8.9E-15 N?
Find the radius of an electrons orbit whenit moves perpendicular to a magnetic field of 0.66t with a speed of 6.27E5 m/s.
Charged particles pass through a velocity selector with electric and magnetic fields at right angles to each other, as shown in the figure. If the electricfield has a magnitudeof 450 N/C and the magnitude field has a magnitude of 0.18T, what speed must the particles have to pass through the selector undeflected?
What is the magnetic force exerted on a 2.15m length of wire carrying a current of 0.899A perpendicular to a magnetic field of 0.720T?
The maximum current in a superconducting solenoid can be as large as 3,750A. If the number of turns per meter in such a solenoid is 3,650, what is the magnitude of the magnetic field it produces?
Two parallel wires, each carrying a current of 2.2A in the same direction, are shown in the figure. Find the direction and magnitude of the net magnetic field at points A, B, and C.
An electron moves at right angles to a magnetic field of 0.18T. What is its speed if the force exerted on it is 8.9E-15 N?
Find the radius of an electrons orbit whenit moves perpendicular to a magnetic field of 0.66t with a speed of 6.27E5 m/s.
Charged particles pass through a velocity selector with electric and magnetic fields at right angles to each other, as shown in the figure. If the electricfield has a magnitudeof 450 N/C and the magnitude field has a magnitude of 0.18T, what speed must the particles have to pass through the selector undeflected?
What is the magnetic force exerted on a 2.15m length of wire carrying a current of 0.899A perpendicular to a magnetic field of 0.720T?
The maximum current in a superconducting solenoid can be as large as 3,750A. If the number of turns per meter in such a solenoid is 3,650, what is the magnitude of the magnetic field it produces?
Two parallel wires, each carrying a current of 2.2A in the same direction, are shown in the figure. Find the direction and magnitude of the net magnetic field at points A, B, and C.
A single conducting loop of wire has an area of 7.2E-2m^2 and a resistance of 110 ohms. Perpendicular to the plane of the loop is a magnetic field of strength 0.48T. At what reate (in T/s) must this field change if the induced current in the loop is to be 0.32A?
A rectangular loop of wire 0.24m by 0.36m is bent into an L shape as shown in the figure. The magnetic field in the vicinity of the loop has a magnitude of 0.035T and points in a direction 25 degrees below the Y-axis. The magnetic field has no x component. Find the magnitude of the magnetic flux through the loop.
phi= BA cos(theta)
phi= (0.035T)(0.24x0.36)(cos25+cos65 degrees)
phi= 4 meters
How do the resistance, capacitive reactance, and inductive reactance change when the frequency in a circuit is increased?
In an a.c. circuit, an inductor produces inductive reactance which causes the current to lag the voltage by 90 degrees. Because the inductor “reacts” to a changing current, it is known as a reactivecomponent. The opposition that an inductor presents to a.c. is called inductive reactance (XL). This opposition is caused by the inductor “reacting” to the changing current of the a.c. source. Both the inductance and the frequency determine the magnitude of this reactance. This relationship is stated by the formula:
A 3.33-kOhm resistor is connected to a generator with a maximum voltage of 141V. Find (a) the average and b. the maximum power delivered to this circuit.
The reactance of a capacitor is 65ohms at a frequency of 57Hz. What is its capacitance?
Find the impedance of a 60Hz circuit with a 45 Ohm resistor connected in series with a 95 uF capacitor.
Predict/Explain When a long copper wire of finite resistance is connected to an ac generator, as shown in figure (a), a certain amount of current flows through the wire. The wire is now wound into a coil of many loops and reconnected to the generator, as indicated in Figure. (a) Is the current supplied,to the coil greater than, less than, or the same as the supplied to the uncoiled wire? (b) Choose the best explanation from among the following.
I. More current flows in the circuit because the coiled wire is an inductor and inductors tend to keep the current flowing in an ac circuit
II. The current supplied to the circuit is the same because the wire is the same. Simply wrapping the wire in a coil changes nothing.
III. Less current is supplied to the circuit because the coiled wire acts as an inductor, which increases the impedance of the circuit.
III. Less current is supplied to the circuit because the coiled wire acts as an inductor, which increases the impedance of the circuit.
An inductor, also called a coil, choke or reactor, is a passive two-terminal electrical component which resists changes in electric current passing through it.
Find the frequency at which a 33 uF capacitor has the same reactance as a 33mH inductor. What is the the resonance frequency of an LC circuit made with this inductor and capacitor?
An electric charge on the r axis oscillates sinusoidally about the origin. A distant observer is located at a point on the *y axis.
(a) In what direction will the electric field oscillate at the observer’s location?
(b) In what direction will the magnetic field oscillate at the observer’s location?
(c) In what direction will the electromagnetic wave propagate at the observer’s location?
Y= Electromagnetic wave
X= Electric field
Z= Magnetic field (oscillates in the plane perpendicular to the electric field and is also perpendicular to the direction of propagation)
- (a) The electric field will oscillate in the x direction
- (b) The magnetic field will oscillate in the z direction.
- (c) The electromagnetic wave will propagate in the positive y direction.
Most of the galaxies in the universe are observed to be moving away from Earth. Suppose a particular galaxy emits orange light with a frequency of 5.000 x 10E14 H2. If the galaxy is receding from Earth with a speed oI 3325 km/s, what is the frequency of the light when it reaches Earth?
NEED TO REWRITE ANSWER! Consider a spiral galaxy that is moving directly away from Earth with a speed V : 3.600 x 105 m/s at its center as shown in Figure 15-26. The galaxy is also rotating about its center, so that points in its spiral arms are moving with a speed of : 6.400 x 105 m/s relative to the center. If light with a frequency of 8.230 x 10^14 H2 is emitted in both arms of the galaxy, what frequency is detected by astronomers observing the arm that is moving (a) toward and (b) away from Earth (Measurements of this type are used to map out the speed of various regions in distant, rotating galaxies.)
Dental X-rays: X-rays produced in the dentist’s office typically have a wavelength of 0.30 nm. What is the frequency of these rays?
Communicating with a Submarine Normal radiofrequency waves cannot penetrate more than a few meters below the surface of the ocean. One method of communicating with submerged submarines uses very low frequenry (VLF) radio waves. What is the wavelength (in air) of a 10.0-kHz VLF radio wave?
The Hale Telescope: The 200-inch-diameter concave mirror of the Hale telescope on Mount Palomar has a focal length of 16.9 m. An astronomer stands 20.0 m in front of this mirror.
(a) Where is her image located? Is it in front of or behind the mirror?
(b) Is her image real or virtual? How do you know?
(c) What is the magnification of her image?
The image is real because its behind the lens
Find the ratio of the speed of light in water to the speed of light in a diamond.
Light enters a container of benzene at an angle of 43 degrees to the normal; the refracted beam makes an angle of 27 degrees with the normal. Calculate the index of refraction of benzene.
(a) Use a ray diagram to determine the approximate location of the image produced by a concave lens when the object is at a distance 1/2 f the lens.
(b) Is the image upright or inverted?
(c) Is the image real or virtual? Explain.
An object is a distance f /2 from a convex lens.
(a) Use a ray diagram to find the approximate location of the image.
(b) Is the lmage upright or inverted? (c) Is the image real or virtual? Explain.
Two lenses that are 35 cm apart are used to form an image, as shown in the figure. Lens 1 is diverging and has a focal length of f1= -7.0 cm; lens 2 is converging and has a focal length f2= 14 cm. The object is placed 24 cm to the left of lens 1.
(a) Use a ray diagram to find the approximate location of the image.
(b) Is the image upright or inverted?
(c) Is the image real or virtual? Explain.
An object is a distance 2f fron a convex lens.
(a) Use a ray diagram to find the approximate location of the image.
(b) Is the image upright or inverted?
(c) Is the image real or virtual? Exphin.
Two lenses that are 35 cm apart used to form an image as shown in the figure. Lens 1 is converging and has a focal length f1= 14cm. Lens 2 is diverging and has a focal length f2- -7cm. The object is placed 24 cm to the left of lens 1.
a. ) Use a ray diagram to find approximate location of the image
b. ) is the image upright or inverted?
c. ) Is the image real or virtual? Explain.
- The image is located just to theleft of lens 2
- The image is inverted
- Since the final image is on the same side of Lens 2 as its object (the original image, which is real), it is VIRTUAL
In Young’s two-slit experiment, the first dark fringe above the central bright fringe occurs at an angle of 0.31 degrees. What is the ratio of the slit separatiory d, to the wavelength of the light?
Light from a He-Ne laser ( wavelength= 632.8 nm) strikes a pair of slits at normal incidence, forming a double-slit interference pattern on a screen located 1.4m from the slits shows the interference pattern observed on the screen. What is the slit separation?
A magnetic field is oriented at an angle of 47 degrees to the normal of a rectangular area 0.051m by 0.068m. If the magnitude flux through this surface has a magnitude of 4.8E-5 Txm^2 what is the strength of the magnetic field?
MRI Soleniod: The magnetic field produced by an MRI solenoid 2.5m long and 1.2m in diameter is 1.7T. Find the magnitude of the magnetic flux through the core of a solenoid.
A solenoid with 385 turns per meter and a diameter of 0.17m has a magnetic flux through its core of magnitude 1.28E-4 Txm^2. Find the current in this solenoid. How would your answer to part a change in the diameter of the solenoid were doubled? Explain.
A single conducting loop of wire has an area of 7.2E-2m^2 and a resistance of 110 ohms. Perpendicular to the plane of the loop is a magnetic field of strength 0.48T. At what reate (in T/s) must this field change if the induced current in the loop is to be 0.32A?
Consider the circuit shown in the figure 23-39. Assuming the inductor in this circuit has the value l= 6.1mH, how much energy is stored in the inductor after the switch has been closed a long time?
This figure shows the magnitude flux through a single loop coil as a function of time. What is the induced emf in the coil at t= 0.05s, t= 0.15s, and t=0.50s?
I= (N)BA = (N)BAcos(Ø) (Usually we don’t use N)
Where N= Number of turns on the wire
At t= 0.05sec
£= -Change in Epsilon/ Change in time > £= (10Wb-0Wb) / (0.1s-0s) £= -100V
*Change value to volts
ON QUIZ: A long straight wire carries a current I, as indicated in the fure. Three small metal rings are placed near the current carrying wire (A and C) or directly on top of it. If the current in the wire is increasing with time, indicate whether the induced emf in each of the rings is clockwise, counterclockwise or zero. Explain your answer for each ring.
Use Right Hand Rule:
Thumb- Force
Pointer Finger- Current
Middle Finger- Magnetic Field
Ring B: Epsilon= BAcos(0) + BAcos(180) = 1 + -1 = 0
Consider the RLC circuit shown in the figure. When the switch is closed, the current in the circuit is observed to increase from 0 to 0.32A in 0.15s. What is the inductance L? How long after the switch is closed does the current have the value 0.50A? What is the maximum current that flows in this circuit?
A rectangular loop of wire 0.24m by 72m is bent into an L shape as shown in the figure. The magnetic field in the vicinity of the loop has a magnitude of 0.035T and points in a direction 25 degrees below the Y-axis. The magnetic field has no x component. Find the magnitude of the magnetic flux through the loop.
An elementary particle called a pi meson (or pion for short) has an average lifetime of 2.6 x 10-8 s when at rest. If a pion moves with a speed of 0.99c relative to Earth
(a) Find the average lifetime of the pion as measured by an observer on Earth and
(b) The average distance traveled by the pion as measured by the same observer.
(c) How far would the pion have traveled relative to Earth if relativistic time dilation did not occur?
The Linac portion of the Fermilab Tevatron contains a high vacuum tube that is 64 m long, through which protons travel with an average speed v=65c. How long is the Linac tube, as measured in the protons frame of reference?
An object has a relativistic momentum that is 7.5 times greater than its classical momentum. What is its speed?
Find the work that must be done on a proton to accelerate it from rest to a speed of 0.90c.
When a proton encounters an antiprotory the two particles annihilate each other, producing two gamma rays. Assuming the particles were at rest when they annihilated, find the energy of each of the two gamma rays produced. (Note: The rest energies of an antiproton and a proton are identical.)
