91Ó°ÊÓ

Figure 32-21.

From Maxwell's law of induction, the relation between magnetic flux induced due to electric field and enclosed current. Then using the right-hand thumb rule, find the directions of the enclosed current in both situations. From this, conclude whether the magnitude$\stackrel{\mathbf{â‡\P Ä}}{\mathbf{E}}$is increasing or decreasing.

The formula is as follows:

role="math" localid="1663041558546" width="200" height="46">∮B⇶Ä.ds⇶Ä=μ0ε0dfEdt=μ0ienc

Maxwell’s law of induction gives

$âˆ\circledR \stackrel{â‡\P Ä}{B}.d\stackrel{â‡\P Ä}{s}={\mathrm{μ}}_0{\mathrm{Î\mu }}_0\frac{d{f}_E}{dt}={\mathrm{μ}}_0{i}_{enc}$

This implies that it $\stackrel{â‡\P Ä}{E}$ is increasing, i_enc is in the direction of the electric field, and vice versa. According to the right-hand thumb rule, i_enc is upward in situation (a) and downward in the situation (b).

Hence, in both situations,$\stackrel{â‡\P Ä}{E}$is decreasing.