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

The rate at which the magnetic field changes is
`(\Delta B )/(\Delta t ) = - 5.33*10^(-3) \ T/ s`

Step-by-step 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 = - (r)/(2) * (\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
`(\Delta B )/(\Delta t )` is the change in magnetic field

So

`(\Delta B )/(\Delta t ) = - (2 * E )/(r)`

substituting values

`(\Delta B )/(\Delta t ) = - (2 * 4.0 *10^(-3))/( 1.5 )`

`(\Delta B )/(\Delta t ) = - 5.33*10^(-3) \ T/ s`