Chapter 31, Problem 1Q

An electric field $\stackrel{\to }{E}$ points away from you, and its magnitude is increasing. Will the induced magnetic field be clockwise or counterclockwise? What if $\stackrel{\to }{E}$ points toward you and is decreasing?

To determine

The direction of induced magnetic field if electric field away from you and increasing.

The direction of induced magnetic field if the direction of electric field is towards you and decreasing.

Answer to Problem 1Q

The direction of magnetic field will be clockwise for both the cases.

Explanation of Solution

Write the expression for displacement current as.

  $I_L=\epsilon \frac{d{\varphi }_E}{dt}$

Here, $I_L$ is the displacement current, $\epsilon$ is the permittivity and $\frac{d{\varphi }_E}{dt}$ is the rate of change of electric flux.

From the above expression it is clear that displacement current is proportional to rate of change of electric flux.

The electric flux is directed away from the observer and is increasing so the direction of displacement current is also away from the observer and therefore the magnetic field will be in clockwise direction.

The electric field is toward the observer and is decreasing so $\frac{d{\varphi }_E}{dt}$ is negative it means the direction of displacement current is opposite to the direction of electric field. So the direction of displacement current will be away from the observer, therefore the direction of magnetic field will be clockwise.

Conclusion:

Thus, the direction of magnetic field will be clockwise for both the cases.