Question

A square loop of side 12 cm and resistance 0.60 $\Omega$ is placed vertically in the east-west plane. A uniform magnetic field of 0.10 T is set up across the plane in north-east direction. The magnetic field is decreased to zero in 0.6 s at a steady rate. The magnitude of current during this time interval is

• A. 1.42 × 10-3 A
• B. 2.67 × 10-3 A
• C. 3.41 × 10-3 A
• D. 4.21 × 10-3 A

Answer 1

Answer: (B)

2.67 × 10-3 A

Answer 2

Here, Area

$A = l^{2} = (12cm)^{2} = 1.4 \times 10^{- 2}m^{2}$

$R = 0.60\Omega B_{1} = 0.10T,\theta = 45{^\circ}$

$B_{2} = 0,dt = 0.6s$

Initial flux $\varphi_{1} = B_{1}A\cos\theta$

$= 0.10 \times 1.4 \times 10^{- 2} \times \cos 45{^\circ}$

$= 9.8 \times 10^{- 4}Wb$

Final flux , $\varphi_{2} = 0$

Induced emf , $\varepsilon = \frac{|d\varphi|}{dt} = \frac{|\varphi_{2} - \varphi_{1}|}{dt}$

$= \frac{|9.8 \times 10^{- 4}|}{0.6s} = 1.6 \times 10^{- 3}V$

Current , $I = \frac{\varepsilon}{R} = \frac{1.6 \times 10^{- 3}}{0.6} = 2.67 \times 10^{- 3}A$