Question

A uniform electric field of magnitude E = 12 N/C points along the x-axis. A circular loop of radius R = 25 cm is centered at the origin with the normal to the loop pointing θ = 15 degrees above the x-axis.

(a) Calculate the electric flux in units of Nm2/C that passes through the loop.

(b) To what angle in degrees relative to the x-axis should the normal of the loop be rotated so that the flux through the loop becomes Φ' = 0.31 Nm2/C?

Answer 1

(a) The electric flux in units of Nm2/C that passes through the loop is

$$\Phi=EA\text{ cos}\theta=E\pi r^2\text{ cos}\theta=2.28\text{ Nm}^2/\text{C}$$

(b) Solve a "backward" problem:

$$\theta=\text{arccos}\frac{\Phi}{E\pi r^2}=82°.$$