Question

Scientists studying an anomalous magnetic field find that it is inducing a circular electric field in a plane perpendicular to the magnetic field. The electric field strength is 4.0 mV/m at a point 1.5 m away from the center of the circle. At what rate is the magnetic field changing?

Answer 1

Answer:

The rate at which the magnetic field changes is  $\frac{\Delta B }{\Delta t } = - 5.33*10^{-3} \ T/ s$

Explanation:

From the question we are told that

   The  electric field strength is $E = 4.0 mV/m = 4.0 *10^{-3} V/m$

   The  radius of the  circular region where the electric field is induced is

   $d = 1.5 \ m$

Generally the induced electric field is mathematically represented as

     $E = - \frac{r}{2} * \frac{\Delta B }{\Delta t }$

The  negative sign show that the induced electric field is acting in opposite direction to the change in magnetic field

Where  $\frac{\Delta B }{\Delta t }$ is the change in magnetic field

So  

       $\frac{\Delta B }{\Delta t } = - \frac{2 * E }{r}$

substituting values

       $\frac{\Delta B }{\Delta t } = - \frac{2 * 4.0 *10^{-3}}{ 1.5 }$

       $\frac{\Delta B }{\Delta t } = - 5.33*10^{-3} \ T/ s$