Question

A circular loop of radius R = 13 cm is centered at the origin in the region of a uniform, constant electric field. When the normal to the loop points in the positive x-direction the flux through the loop is Φ1 = 25 N•m2/C. When the normal to the loop points in the positive y-direction the flux through the loop is Φ2 = -75 N•m2/C. When the normal to the loop points in the positive z-direction the flux though the loop is zero.
Calculate the x-component of the electric field, in newtons per coulomb.

Answer 1

Answer:

Electric field, $E_x=470.87\ N/C$

Explanation:

It is given that,

Radius of the circular loop, r = 13 cm = 0.13 m

Electric flux in the positive x direction, $\phi_x=25\ Nm^2/C$

Electric flux in the positive y direction, $\phi_y=-75\ Nm^2/C$

The formula of the electric flux is given by :

$\phi=EA$

In x- direction, $\phi_x=E_x\times \pi r^2$

Where, $E_x$ is the electric field in x direction.

$E_x=\dfrac{\phi_x}{\pi r^2}$

$E_x=\dfrac{25}{\pi (0.13)^2}$

$E_x=470.87\ N/C$

So, the  x-component of the electric field is 470.87 N/C. Hence, this is the required solution.