A conducting circular loop is placed in a uniform magnetic field, B=0.025 ~T with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of 1 mms ⁻¹ . The induced emf when the radius is 2 ~cm , is

Step-by-step solution

Given: The magnetic field in the region is, ( B =0.025 ~T ). Radius of the loop, ( r =2 ~cm =2 10⁻² ) Constant rate at which radius of the loop shrimks, ( dr dt =1 10⁻³ ~ms ⁻¹ ) To find: The induced emf in the loop when radius is 2 cm. The magnetic flux linked with the loop is given by: ( aligned & = BA & = B ( r ^2 ) O ^ & B r ^2 aligned ) The magnitude of induced emf is given as: ( aligned & | |= d dt & = d dt ( B r ^2 ) & = B 2 r dr dt aligned ) Substitute the values. ( aligned & | |=0.025 2 2 10⁻² 1 10⁻³ & = 10