A circular loop of radius R = 3 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 = 85 N•m2/C. When the normal to the loop points in the positive y-direction the flux through the loop is Φ2 = -85 N•m2/C. When the normal to the loop points in the positive z-direction the flux through the loop is zero.

The Questions are

a. Calculate the x-component of the electric field, in newtons per coulomb

b. Calculate the y-component of the electric field, in newtons per coulomb

c. Calculate the z-component of the electric field, in newtons per coulomb

d. Calculate the magnitude of the electric field, in newtons per coulomb.

Explanation:

Given that,

Φx= 85 N•m2/C. X direction

Φy= -85 N•m2/C. Y direction

Φz = 0. Z direction

Radius of loop =3cm=0.03m

Surface area of the circle is πr²

A=22/7×0.03²

A=0.00283m²

Flux is given as Φ=EA

a. Φx=ExA

Ex=Φx/A

Ex=85/0.00283

Ex=30035.33N/C

b. Ey=Φy/A

Ey=-85/0.00283

Ey=-30035.33N/C.

c. Ez=Φz/A

Ez, =0/A

Ez=0N/C

d. Magnitude of E.

E=√Ex²+Ey²+Ez²

E=√(30035.33)²+(-30035.33)²

E=42476.38N/C.

they start with the same