Question

An equilateral triangle $ABC$ of side a is placed in the magnetic field with side $AC$ and its centre coinciding with the centre of the magnetic field. The magnetic field varies with time as $B=ct$. The electromotive force induced across side $AB$ is:-

• A. $\frac{\sqrt{3}}{4}{a}^{2}c$
• B. zero
• C. $\frac{a^{2}c}{4\sqrt{3}}$
• D. $\frac{(\sqrt{2}-1)}{4}{a}^{2}c$

Answer 1

The correct option is C $\frac{a^{2}c}{4\sqrt{3}}$

Consider a circle increasing triangle ABC

$r\cos {30}^o=\frac{a}{2}$

$r=\frac{\sqrt{3}}{2}=\frac{9}{2}$

$\Rightarrow r=\frac{4}{\sqrt{3}}$

$\Rightarrow E.2\pi r=\pi r^2.\left(\frac{dB}{Dt}\right)$

$\Rightarrow E.2=rc$

$\Rightarrow E=\frac{rc}{2}=\frac{ac}{2\sqrt{3}}$

$therefore(E.\cos {30}^o)\times a=(VA-VB)$

$(VA-VB)=\frac{ac}{2\sqrt{3}}.\frac{1}{2}.a$

$=\frac{a^{2}c}{4\sqrt{3}}$

Hence, option $C$ is correct answer.