Electric Charges and Fields — Practice

Question 1

Charges 2 uC and -2 uC are 1 cm apart. Find the field at 50 cm on the perpendicular bisector.

Accepted Answer

This is the equatorial point with p = q(2a) = 2e-6 x 0.01 = 2e-8 C m. E = kp/r^3 = 9e9 x 2e-8 / 0.125 = 1440 N/C, opposite to p.

Question 2

An infinite line charge has linear density 5 uC/m. Find the field at 10 cm.

Accepted Answer

E = lambda/(2 pi epsilon0 r) = 5e-6/(2 pi x 8.85e-12 x 0.1) approximately 9e5 N/C.

Question 3

Find the flux through a cube of side 0.1 m with 10 uC at its centre.

Accepted Answer

Flux = q/epsilon0 = 10e-6/8.85e-12 = 1.13e6 N m^2/C, independent of the cube's size.

Question 4

A conducting sphere of radius 0.1 m carries 5 uC. Find E at r = 0.05 m and r = 0.3 m.

Accepted Answer

Inside the conductor E = 0. Outside, E = kQ/r^2 = 9e9 x 5e-6 / 0.09 = 5e5 N/C.

Question 5

A dipole (p = 1e-7 C m) is at 30 degrees to a field of 2e4 N/C. Find torque and potential energy.

Accepted Answer

Torque = pE sin(theta) = 1e-7 x 2e4 x 0.5 = 1e-3 N m. U = -pE cos(theta) = -1e-7 x 2e4 x 0.866 = -1.73e-3 J.

Practice — Electric Charges and Fields