A current `I(=4A)` flows along a thin wire PQRS shaped as shown in figure. The radius of the curved part of the wire is `10*0cm`. The angle `theta=90^@`. Find the magnitude of the total magnetic field at the point O.

Options

A. `28 xx 10^(-4)T`
B. `2.8 xx 10^(-7)T`
C. `28 xx 10^(-6)T`
D. `2.8 xx 10^(-6)T`

Answer

C

Explanation

The magnetic field at the centre O of the coil is, `B_(0) = (3)/(3) .(mu_(0)I)/(2R) + (mu_(0)I)/(4pi r) [sin 45^(@) + sin 45^(@)]`
`rArr B_(0) = (3)/(4).(4pi xx 10^(-7) xx 5)/(2 xx 12 xx 10^(-2)) + (4pi xx 10^(-7) xx 5 xx 2 sin 45^(@))/(4pixx 12 cos 45^(@) xx 10^(-2))= 28 xx 10^(-6)T`