Question

A conducting circular loop is placed in a uniform magnetic field 0.04T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2mm/sec . The induced emf in the loop when the radius is 2cm is

A. 3.2πμV
B. 4.8πμV
C. 0.8πμV
D. 1.6πμV

Answer 1

The induced emf in a shrinking conducting circular loop placed in a uniform magnetic field is calculated using Faraday's Law of Electromagnetic Induction by determining the rate of change of the loop's area.

Step-by-step explanation:

The induced emf in a loop due to a changing magnetic field can be calculated using Faraday's Law of Electromagnetic Induction, which states that the emf induced in a loop is equal to the negative change in magnetic flux through the loop over time. For a conducting circular loop with a decreasing radius, the change in flux is a result of the change in area as the radius shrinks. Given a uniform magnetic field of 0.04 T, and knowing the rate of shrinkage of the radius is 2mm/sec or 0.002 m/sec, and at the moment we are interested in, the radius is 2cm or 0.02 m, the induced emf can be calculated using the formula:

emf = -dΦ/dt = -B*(dA/dt)

where B is the magnetic field strength and A is the area of the loop. In this scenario, the induced emf when the radius of the loop is 2cm can be found by first calculating the rate of change of area (dA/dt) due to the shrinking radius then applying Faraday's Law.