Question

A triangular wire frame ABC (each side=2m) is placed in a region of time variant magnetic field having $dB/dt=\sqrt{3}T/s$. 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 potential difference between the points A and B will be

• A. $0.4V$
• B. $0.6V$
• C. $1.2V$
• D. None

Answer 1

The correct option is B $0.6V$

Given

A triangular wire of side 2m

Magnetic field is perpendicular to the frame

Rate of change in magnetic field dB/dt is given

resistance of base AB is 1 ohm and other two sides are 2 ohm

Solution

Area of triangular frame =$A=\frac{3^{\frac{1}{2}}}{4}\ast 2^2=3^{\frac{1}{2}}$

Magnetic flux=$\varphi =B\ast A$

Induced EMF=$\frac{d\varphi }{dt}=A\ast \frac{dB}{dt}=3^{\frac{1}{2}}\ast 3^{\frac{1}{2}}=3$

Total resistance=5ohm

Induced current =EMF/Resistance=3/5=0.6A

Resistance of wire AB= 1ohm

Potential difference of AB is 0.6*1ohm=0.6V

The correct option is B