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The circular wire in figure below encircles solenoid in which the magnetic flux is increasing at a constant rate out of the plane of the page. The clockwise emf around the circular loop is $\varepsilon_{0}$. By definition a voltammeter measures the voltage difference between the two points given by $V_{b}-V_{a}=-\int \limits_{a}^{b} E \cdot d s$ We assume that $a$ and $b$ are infinitesimally close to each other. The values of $V_{b}-V_{a}$ along the path $1$ and $V_{a}-V_{b}$ along the path $2$ , respectively are
$-\varepsilon_{0},-\varepsilon_{0}$
$-\varepsilon_{0}, 0$
$-\varepsilon_{0}, \varepsilon_{0}$
$\varepsilon_{0}, \varepsilon_{0}$
Solution
$(b)$ Given, $V_{b}-V_{a}=-\int \limits_{a}^{b} E \cdot d s$
As we know,
$\oint E \cdot d s =-\frac{d \phi}{d t}=\varepsilon_{0}$
$\therefore$ For path $1, V_{b}-V_{a}=-\varepsilon_{0}$
and for path $2, V_{b}-V_{a}=0$ (as flux enclosed is zero)
