Electric Charges and Fields

Question 1

What are the properties of electric charges?

Answer 1

Quantisation, Additivity, Conservation

Question 2

State the similarities and differences between Electrical and Gravitational forces

Answer 2

Both follow the inverse square law

Gravitational forces are independent of media and are always attractive, whereas Electrical forces depend on media and can either be attractive or repulsive

Question 3

State Coulomb’s law in vector form. What is the proportionality constant? Give its value in SI units.

Answer 3

F = k . q1q2 . (r2-r1) / (r^3)

The proportionality constant is 1/4pi€0, or k. Its value is 9 x 10^9 N m^2 C^-2

Question 4

Give the expression of the Electric field generated by a test charge ‘q’ in vector form.

Answer 4

E = k . q. r / (r^3)

Question 5

What is the value of electric field inside a conductor, and why?

Answer 5

0; charges rearrange themselves in such a way that they cancel the effect of the external electric field, and then come to a standstill.

Question 6

Point of equilibrium of a charge when kept between 2 like charges, and 2 unlike charges

Answer 6

sqrt(|q1|)/(sqrt(|q2|)+sqrt(|q1|))

sqrt(|q1|)/((sqrt(|q2|)-sqrt(|q1|))

Question 7

Electric field at a point P at a distance ‘a’ away, axially, from one end of a rod of length ‘L’.

Answer 7

k . q / (a(a+L))

Question 8

Electric field at a point P at a distance ‘x’ away, axially, from the centre of a uniformly charged ring (+Q) of radius R.

Answer 8

k . Q . x /((R^2+x^2)^(3/2))

Question 9

Electric field due to a long thin rod of charge density Lamba at a point P, which is ‘a’ units away from the rod.

Answer 9

2 . k . Lambda / a

Question 10

State Gauss’ law. What if the formula of Electric flux?

Answer 10

∮E.dA = q(in)/ε0

Φ=E.A

Question 11

A charge +Q is kept at the centre of an arc (θ, R). Find the E through its centre.

Answer 11

(2 . k . λ / R) . sin(θ/2)

Question 12

E inside, and on the surface of a nonconducting a) shell and b) sphere, and inside a conducting c) shell and d) sphere

Answer 12

a) 0
b) 0
c) 0
d) (k . σ / 2) . (3R^2 - x^2), where R is the radius of the sphere, and x is the distance from the centre

Question 13

E outside a nonconducting a) shell b) sphere and conducting a) shell b) sphere

Answer 13

a), b), c), d): (k . Q / x), where x is the distance from the centre of the sphere / shell