A current carrying wire is placed in the grooves of an insulating semicircular disc of radius 'R', as shown in Fig. The current enters at point A and leaves from point B. Determine the magnetic field at Point D.

Options

A. `(mu_(0)i)/(8piRsqrt(3))`
B. `(mu_(0)i)/(4piRsqrt(3))`
C. `(sqrt(3)mu_(0)i)/(4piR)`
D. None of these

Answer

B

Explanation

`r_(1)=2R sin 30^(@)=R,r_(2)=2Rsin60^(@) =R`

`B_(D)=B_(AC)+B_(CB)`
`=(mu_(0))/(4pi)[i/(r_(1)) sin phi_(1)]. +(mu_(0))/(4pi)[i/(r_(2)) sin phi_(2)]ox`
`=(mu_(0))/(4pi) i[(sin60^(@))/(r_(1))-(sin 30^(@))/(r_(2))]. =(mu_(0)i)/(4piRsqrt(3)).`