A small current carrying loop having current i is placed in the plane of the paper as shown Anothersemicircular loop having current `i_0` is placed concentrically in the same plane as that of the small loop, the radius of semicircular loop being `R(Rgt gt a)`. Find the force applied (in newton)by the smaller ring on the bigger ring. `(Given R=1m, i=i_0=40/(mu_0)A, a=0.1m)`

Answer

`8N`

Explanation

Magnetic field due to smaller ring at distance R (equatorial point )
from the centre `B=((mu_0)/(4pi))M/(R^3) where M=ipia^2`
`:. B=((mu_0)/(4pi)) (ipia^2)/(R^3)=(mu_0ia^2)/(4R^3)`
`dF=i_0Rd theta (mu_0ia^2)/(4R^3)`
`dF_x=dF sin theta=(mu_0i i_0a^2sin theta d theta)/(4R^2)`
`F_x=(mu_0i i_0a^2)/(4R^2) int_0^(pi) sin theta d theta`
`implies F_x=(mu_0i i_0a^2)/(4R^2)xx2=(mu_0i i_0a^2)/(2R^2), and F_y=0`
`:. F_(n et)=F_x=(mu_0i i_0a^2)/(2R^2)=8N`