Question

Example 6.2 A square loop of side 10 cm and resistance 0.5 l is
placed vertically in the east-west plane. A uniform magnetic field of
0.10 T is set up across the plane in the north-east direction. The
magnetic field is decreased to zero in 0.70 s at a steady rate. Determine
the magnitudes of induced emf and current during this time-interval.​

Answer 1

Answer:

The induced emf is 1.01 × 10-3 V and the current is  2.02 × 10^(-3) A

Explanation:

According to the problem the side of the loop is 10 cm or 0.1 m

and the resistance of the square loop is 0.5 I

The magnetic field , B = 0.10 T

Therefore Area of the loop is , A = (0.1)^2m = 0.01 m

As the current is flowing in east- west direction and the magnetic field is set at north to east direction

Therefore the angle between them, θ = 45°

Therefore,

The magnetic flux,

ϕ = A x B x  cosθ

   = (0.01)(0.1)(cos45)

     = 7.07 × 10-4 Wb

According to the problem the magnetic field is decreased to zero in 0.70 s

Therefore, the induced emf = e = -dϕ/dt = -(7.07 × 10-4)/0.70

e = -1.01 × 10-3 V

Therefore the current within the loop = 1.01 × 10-3/0.5 = 2.02 × 10^(-3) A