The magnets of two suspended coil galvanometer are of the same strength so that they produce identical uniform magnetic fields in the region of the coils. The coil of the first one is in the shape of a square of side a and that of the second one is circular of radius `(a)/(sqrtpi)`. When the same current is passed throught the coils, the ratio of the torque experienced by the first coil to that rxperienced by the second one is

Options

A. `1: (1)/(sqrtpi)`
B. `1:1`
C. `pi :1`
D. `1: pi`

Answer

B

Explanation

Given : Radius of the circulat ring `= (a)/(sqrtpi)` Slide of the square= a The strength of magnetic field produced by two coils is same. As torque experienced by any coil, `tau= BIA cos theta`
`:.` Magnetic field is uniform in nature.
`:. ("Torque experienced by the first rectangular coil")/("Torque experience by the circular coil")= (BIA_(1) cos theta)/(BIA_(2) cos theta)`
`=(a^(2))/(pi ((a)/(sqrtpi))^(2))= (1)/(1)=1`