Electric Fields Flashcards
What is an electric field?
A region of space in which a charged particle experiences a force with its strength described as E
Describe the relationship between Field strength, force and charge and state the equation.
Electric field strength at a point in space is equal to the force per unit charge on a small positive test charge placed in that position. E= F/Q
What direction are the field lines of a positive point charge?
Out of/ away from the charge
What direction are the field lines of a negative point charge?
Into/ towards the charge
What unit is E, electric field strength, measure in?
N.C^-1 or V.m^-1
(Newtons per coulomb or Volts per metre)
What is the relationship between distance and radial field strength?
As the distance from the source of the charge increases, the strength decreases (the lines are radial and so grow further apart)
What is coulombs law?
The electrostatic force between two charges is directly proportional to the product of the charges; it is inversely proportional too the square of the distances between them.
What is the equation for electrostatic force (coulombs law)
F = (k.Q1.Q2) / r²
For radial fields ONLY, how do you calculate the electric field strength?
E = kQ / r²
What is the electric potential?
The electric potential at a a point in a field is equal too the work done per unit charge in moving a small positive test charge from infinity too that point.
WORK DONE PER UNIT CHARGE
What unit is electric potential measured in?
V (volts) or J/C
What value is measured by taking the area under a field strength against distance graph?
Theoretical potential
What is the equation for the electric potential?
Ve = k.Q / r
What value can be taken as the area under a force against distance graph? (between two points)
Work done in moving a charge q from r1 to r2
What is the equation for the work done in moving a charged particle?
ΔVe * q
(change in electric potential)
What value can be taken as the gradient of a Electric potential (Ve) against distance graph?
E - electric field strength
If a positive charge q is placed in a field, what direction is the force upon it in relation to the electric field?
The same direction as E, otherwise it is in the opposite direction.
(-ively charged)
What is the electrical potential at infinity?
0V, by definition, Ve of a point in space is the work done moving a small positive test charge from infinity to that point.
What equations apply too all fields? (F and W)
F = EQ and ΔW = q.ΔV
What is the numerical value of the constant k?
8.99 x 10^9 Nm²C-²
What is the equation for the electrical potential energy? EPE
(k.Q.q) / r
When a point charge is moved from a source, what energy transfer occurs?
The change in EPE is equal too the kinetic energy gained. (EPE decreases as the distance from the source increases)
What is an equipotential?
A surface on which the electrical potential (Ve) is constant
For a lone charge, how are equipotentials represented?
Spherical shells around the charge
As the equipotentials grow further apart, what happens to E?
E decreases in strength
What is the direction of the field strength relative too an equipotential?
Perpendicular, pointing in the direction of decreasing potential (towards the -ive charge)
What is a capacitor?
Electrical component which can store charge and energy by using an electric field
What is capacitance?
Amount of charge that must be stored on the plates to provide a 1V potential difference between them.
What is the unit for capacitance? What is the typical prefix of a value of capacitance?
F, Farads. Micrometres.
How do you find the capacitance from a Charge on capacitor / Potential difference across capacitor graph?
Gradient of the line through the origin
How do you find the energy stored in a capacitor from a Charge on capacitor / Potential difference across capacitor graph?
Area underneath it
(E = 1/2 Q.V) (ΔW = q.ΔV)
What are the formulas for energy stored in a capacitor?
E = 1/2 Q.V = 1/2 C.V² = 1/2 Q²/C
What effects the charge that can be held by a parallel plate capacitor?
Plate separation (closer together, more charge)
Area of the plates (higher area, more charge)
Inserting a dielectric
What is the capacitance of a parallel plate with a dielectric?
C = A. Ɛ0. Ɛr / d
A= area overlapping the plates
Ɛ0 = permittivity of free space
Ɛr = dielectric constant
What is the equation for the permittivity of a material Ɛ?
Ɛ = Ɛ0. Ɛr
What is a dielectric made of?
Polar molecules
How does dielectric action work?
The polar molecules rotate too align their negative poles to the positive poles of the plates.
The electric field of the polar molecules opposes the electric field of the plates decreasing the resultant electric field.
E = V/d so as E decreases V decreases.
Where Q is kept constant, C = Q/V, The capacitance then increases.
What is the equation for the capacitance without a dielectric inserted?
C = A.Ɛ0 / d
When charging a capacitor, what is the initial potential difference across the capacitor plates?
0
When charging a capacitor, what is the final/maximum potential difference across the capacitor plates?
Ɛ (emf)
What law states the conservation of potential difference?
Kirchoffs voltage law
What is the Ɛ equal too? (Vc,Vr)
Ɛ = Vc + Vr
What decay occurs upon Charge and Voltage of the capacitor when charging in relation too time?
What are the equations?
Positive exponential
Vc(t) = Ɛ(1- e^-t/RC)
Q(t) = Qmax (1- e^-t/RC)
What equations link V,I,R,C and Q?
V=I.R
Vr(t) = I(t). R
Ɛ = I0.R
Q = V.C
Vc(t) = Q(t) / C
What is current?
The rate of change of charge
dQ/dt
How do you calculate the time constant?
R.C
What is the initial current in the circuit when charging a capacitor?
I0 = maximum current
How do the voltage of the exterior resistance and current of the circuit decay? What are the equations in relation too time?
Negative exponential (decay)
Vr(t) = Ɛ.e^(-t/R.C) as Vr (0) = Ɛ
I(t) = I0.e^(-t/RC)
When a capacitor is discharging, by what law are the Vc = Vr (or exterior voltage)?
kirchoffs voltage law
How do the current in the circuit, charge stored and Pd between the plates decay when a capacitor is discharging? Why?
Vc(t) = V0.e^(-t/RC)
Q(t) = Q0.e^(-t/RC)
I(t) = I0.e^(-t/RC)
Vc(t) is directly proportional too Q(t)
I(t) is directly proportional too Vc(t)
What happens if the time constant is larger?
Decay is slower as 1/RC is a smaller exponent
What is the time taken for voltage current or charge to half when discharging a capacitor?
t1/2 = ln(2).R.C
What is the equation of the decay of energy stored relating too time when a capacitor is being discharged? Derive it.
E(t) = E0 . e^(-2t/RC)
E(t) = 1/2. Q(t). V(t)
E(t) = 1/2 . Q0. V0 . (e^-t/RC)^2
1/2. Q0.V0 = E0
sooo
E(t) = E0 . e^(-2t/RC)
What is the time taken for energy stored to half when discharging a capacitor?
t1/2 = ln(2) .R.C /2 (as exponent is double)
