A long solenoid with 2000 turns per meter has a small loop of radius (3 ~cm ) placed inside the solenoid normal to its axis. If the current through the solenoid increases steadily from (1.5 ~A ) to (5.5 ~A ) in ( ^2 100 ~s ), the induced emf in the loop is

Step-by-step solution

Key idea Magnetic field inside a solenoid of infinite length is given by expression (B= ₀ n i ) where, (n= ) number of turns per unit length. Given, number of turns in solenoid, (n=2000 ), current through solenoid, (i_i=1.5 ~A ) and (i_f=5.5 ~A ) So, ( B= ₀ n (i_f-i_i ) ) Putting the given values, ( aligned & =4 10⁻⁷ 2000(5.5-1.5) B & =4 10⁻⁷ 2000 4 aligned ) Now, emf induced in a loop of radius (3 ~cm ), ( gathered e=- d d t = B A t e= 4 10⁻⁷ 2000 4 (3 10⁻² )^2 ( 0^ ) ^2 100 E=0.288 mV ( =0^ ) gathered ) Hence, th