0
Closed
Induced magnetic field from non-uniform electric field
An electric field is directed out of the page within a circular region of radius R=3.00 cm. The magnitude of the electric field is given by E = (.500 V/m*s)(1-r/R)t, where t is in seconds and r is the radial distance (r<=R). What is the magnitude of the induced magnetic field at radial distance 5.00 cm?
Customer support service by UserEcho
Using one of maxwell's equations in integral form
integral(B*dl) = mu_0*epsilon_0 integral(dE/dt * da)
Apply the bounds for dl as 0 to 2 pi and for da as 0 to R and 0 to 2pi.
After integrating, you find the integral on both sides after applying the derivative with respect to time of the Electric field.
Student 5051 is correct. integrating and solving for the magnetic field at R' should give:
B= (1/3)*mu*epsilon*(3R'/2 - R'^2/R)
Good luck!