An electric field of 100 V/m is directed outward from the plane of a circular area with radius 4.0 cm.If the electric field increases at a rate of 10 V/ms,determine the magnitude of the magnetic field at a radial distance 10.0 cm away from the center of the circular area.

Question

Quizplus · Accepted Answer

The magnetic field at a radial distance R away from the center of the circular area is given by:

B = μ0I / (2R)

where μ0 is the permeability of free space and I is the current enclosed by the circular area.

Since the electric field is increasing at a rate of 10 V/ms, the induced electric field is given by:

E = -dΦB / dt

where ΦB is the magnetic flux through the circular area.

The magnitude of the induced electric field is equal to the magnitude of the rate of change of the magnetic flux:

|E| = |dΦB / dt| = πR^2 |dB / dt|

Since the electric field and the magnetic field are perpendicular to each other and to the plane of the circular area, we have:

E = cB

where c is the speed of light.

Therefore, we can write:

|B| = |E| / c = πR^2 |dB / dt| / c

Substituting the given values, we get:

|B| = π(0.1)^2 × 10 / (3 × 10^8)

|B| ≈ 8.9 × 10^-16 T

Therefore, the best choice is D.

An Electric Field of 100 V/m Is Directed Outward from the Plane