Chapter 16 - Charge & Field Flashcards
What are electric fields caused by?
Any object with charge has an electric field around it which interacts with other electrically charged particles
What is Coulomb’s Law?
A law used to calculate the force between two point charges
F = kQq/r^2
What is k?
k is Coulomb’s constant.
k = 8.99 x 10^9 Nm^2C^-2
What is epsilon?
permittivity of material between charges
What can be said about the forces on each point charge Q and q
Equal and opposite
What is electric field strength?
Force per unit positive charge
the force that a charge of +1 C would experience in an electric field
Electric field strength
E = F / q in NC^-1
E = V / d in Vm^-1
What is a point charge?
A body which behaves as if all its charge is concentrated at the centre
What is the force on a charge in a uniform electric field?
F = qE = qV/d
What can the electric field be described as?
Rate of change of electrical potential with respect to distance
E = dV/dx
For point charges what are their electric fields like?
Radial fields where E is a vector pointing in the direction a positive charge would move
Formula for electric field
E = F / q
Therefore
E = kQ/r^2
What is the relationship between the electric field and the electric potential (voltage)
Voltage is the integral of the electric field (i.e area under the graph)
What is the relationship between the force and the EPE?
EPE is the integral of the force
How can you tell the strength of an electric field in a diagram?
Field lines are more closely packed together when the field is stronger.
Formula for EPE
EPE = kQq/r
What is the electric potential energy?
The work that would need to be done to move a small charge (q) from infinity to a distance (r) away from point charge (Q)
Derivation of voltage formula from EPE
Since E = qV, V = E/q
Therefore V = kQ/r
What is the electric potential?
Electric potential energy per unit positive charge
What did Milikan’s experiment show?
Showed that charge was quantised and came in discrete “packets” of size 1.6 x 10^-19 C (Fundamental unit of charge - one elctron)
How did Milikan discover this?
Watched oil drops for which F = qE = mg.
Found charge to be equal to n x e
Within a spherical point charge how does the voltage and the electric field strength change?
Electric field strength = 0 inside of the sphere
Voltage remains at a constant value from the surface of the sphere to the center.
Max angle of deflection in electric and magnetic fields
Electric field: 180 degrees due to a constant magnitude force (F = QE) in a constant direction
Magnetic fields: 360 degrees as there is a constant magnitude force BUT always perpendicular to the velocity
Electron gun equation
v = root(2QV/m)
Can be derived from: E = QV = 1/2 mv^2 since a particles energy is converted to kinetic energy with acceleration.
Why are charged particles in magnetic fields always deflected in circular paths?
Due to fleming’s left hand rule, the force on a moving charge (in a magnetic field) is always perpendicular to the velocity (i.e direction of travel).
Why is the radius of curvature of the path of a deflected charged particle important?
Gives you information about the particle’s charge and mass.
Hence, different particles can be identified by studying their deflections in a magnetic field.
What is the equation for the radius of curvature?
r = mv/qB
Total energy of a free particle
Kinetic energy + rest energy
E total = ymc^2
Calculation of the relativistic factor
E total / E rest = y mc^2 / mc^2 = y
In linear accelerators, why does the distance between electrodes increase?
Because as the particles accelerate, their velocity increases and hence they travel a larger distance in the same time so they travel further per oscillation of the current. (alternating current which switch charge)
Why do particles in magnetic fields spiral?
As they collide with other particles and lose energy and thus their velocity decreases.
Since velocity is proportional to radius ( r = mv/Bq ) their radius decreases with velocity.
How can a particle travel in a straight line in a velocity selector?
Only if the electric force on it is equal and opposite to the magnetic force on it.
F = qE = qvB
