Question

A triangular wire frame, each side of $2m$ is placed in a region of time variant magnetic field having $\frac{dB}{dt}=\sqrt{3}T/s$ . The magnetic field is perpendicular to the plane of the triangle. The base of the triangle $AB$ has a resistance $1\Omega$ while the other two sides have resistance $2\Omega$ each. The magnitude of the potential difference between the points $A$ and $B$ will be
(Note: Magnetic field is absent inside the triangular loop)

• A. $0.2V$
• B. $0.6V$
• C. $0.8V$
• D. $1.2V$

Answer 1

The correct option is A $0.2V$


$E=\frac{d\varphi }{dt}=A\frac{dB}{dt}=\frac{1}{2}\times 2\times \frac{\sqrt{3}}{2}\times \sqrt{3}$

$\Rightarrow E=\frac{3}{2}V$

$R_{total}=5\Omega$

$I=\frac{E}{R_{total}}=\frac{3}{10}A$


$V_A-\frac{3}{10}\times 2+0.5=V_B$
$V_B-V_A=1-\frac{3}{5}$
$=0.4V$