Electric Potential and Capacitance

Question 1

Potential due to a charge +Q at a distance ‘r’ from it

Answer 1

V = k . Q / r

Question 2

If V = ((r^3)/3)) - 4r^2 + 6r - 2, find E at r=2m

Answer 2

E = -dV/dr

Question 3

What is the potential due to a uniformly charged ring on its axis?

Answer 3

V = k . Q / ((R^2+x^2)^(1/2))

Question 4

What is the potential due to a uniformly charged disc at a point on its axis

Answer 4

V = (σ/2ε0) . (1- (x/((R^2+x^2)^(1/2))), or (1- cosθ)

Question 5

Potential inside and outside nonconducting and conducting shells and spheres

Answer 5

Shells (outside): k . Q / r, where r is the distance from the centre
Shells (inside): always k . Q / R, where R is the radius of the shell (because the E is 0)

Spheres (outside): k . Q / r
Conducting spheres (inside): k . Q / R
Nonconducting spheres (inside): (σ/2Rε0) . (3R^2 - x^2), where x is the distance from the centre

Question 6

Potential Energy of an electric dipole and torque experienced by it when kept in a uniform E.

Answer 6

U = -p.E

T=pxE

Question 7

Dipole moment of a +2Q, -2Q pair at a distance r/4 from each other

Answer 7

P = Q/2

Question 8

Electric field vector due to a dipole at an axial position and equatorial position. Also, state the E and V of a dipole at an angle θ to it.

Answer 8

E= 2kp/r^3, E=-kp/r^3

E=(kp/r^3)(1+3cos^2(θ))

V=kpcos(θ)/r^2

Question 9

KCL is based on ______ and states _______.

KVL is based on ______ and states _______.

Answer 9

The Law of Conservation of Charge; the sum of currents entering and exiting a junction point are the same

The Law of Conservation of Energy; Potential difference in a closed loop is 0

Question 10

F, E, C, and U of a parallel plate capacitor kept in a medium of dielectric constant K.

Answer 10

(Q^2)/(2ε0A.K); Q/(2ε0A.K); Kε0A/d; 1/2 Kε0 E^2

Question 11

Battery disconnected slowly and fast- what remains constant in each case?

Answer 11

Slowly- Charge, Fast- Potential difference

Question 12

C of a Capacitor with a partially filled dielectric.

Answer 12

C = ε0A/(d-t+t/k)

Question 13

2 spheres: (C1, Q1, R1) and (C2, Q2, R2) come in contact with each other. Find their final Capacitances and Charges

Answer 13

V(f) = C1V1+C2V2/(C1+C2)

Q1+Q2=Q1’+Q2’

C=R/k for spheres of radius R