Question

The endpoints of a conducting string (shaped as a circular loop) of constant length are being pulled at constant velocity v. There exists a uniform magnetic field B in space which is perpendicular to circular loop. If the loop always remains circular during motion of its endpoints, then the emf induced in the loop at t = πR/2v is

Answer 1

Explanation:

Given The endpoints of a conducting string (shaped as a circular loop) of constant length are being pulled at constant velocity v. There exists a uniform magnetic field B in space which is perpendicular to circular loop. If the loop always remains circular during motion of its endpoints, then the emf induced in the loop at t = πR/2v is

• Now there is a string and it is being pulled on both sides. So both ends are pulled with a speed equal to v.
• Then the circumference is decreasing by 2v
• So the time is given by t = π R / 2v
•                      Now circumference = 2πR – 2v x πR/2v
•                                                       = πR
• Therefore new radius = 2πr = πR
•                             Or r = R/2
•              Induced emf e = - B dA / dt
•                                       = - B 2πr dr/dt
•                          Now 2πdr/dt = v
•               So e = - Brv

Reference link will be

https://brainly.in/question/12775671