Question

Figure shows three regions of magnetic field, each of area A, and in each region magnitude of the field decreases at a constant rate $‘{\alpha }^{\prime }$. If $\overrightarrow{E}$ is induced electric field then value of line integral $\oint \overrightarrow{E}.d\overrightarrow{r}$ along the given loop is equal to

• A. $\alpha A$
• B. $-\alpha A$
• C. $3\alpha A$
• D. $-3\alpha A$

Answer 1

The correct option is B

$-\alpha A$

$\int \overrightarrow{E}.d\overrightarrow{r}=-\frac{d\varphi }{dt}$ and take the sign of flux according to right hand curl rule get. $\int \overrightarrow{E}.d\overrightarrow{r}=-(-(-\alpha A)-(-\alpha A)+(-\alpha A\left)\right)=-\alpha A$