A rectangular loop ABCD is made of a uniform wire. The side lengths are AB = CD = L and AD = BC = w . In Case 1, a steady current I enters the loop at A and leaves at C . In Case 2, the same steady current I enters at A and leaves at B . If the ratio of the magnetic force per unit length between the sides AB and CD in Case 1 to that in Case 2 is 25:24 , the ratio of the side lengths L w is:

Step-by-step solution

In Case 1, the current I splits into two parallel paths ABC and ADC . Both paths have the same length L+w , so the current divides equally. Current in side AB , I_ AB = I 2 Current in side CD , I_ CD = I 2 The magnetic force per unit length between AB and CD is f₁ I_ AB I_ CD = I^2 4 . In Case 2, the current I splits into path AB (length L ) and path ADCB (length L+2w ). The equivalent resistance of the loop is proportional to its length. Using the current divider rule: Current in side AB , I'_ AB = I L+2w 2L+2w Cu