A current I is flowing through a loop. The direction of the current and the shape of the loop are as shown in figure. Let the magnitude magnetic field at the centre of the loop is found to be Q times `( mu _(0) I )/(R ).` What should be the value of Q?
(Here `MA = R< MB = 3 R, angle DMA = 90^(@)`)

Answer

`00.42`

Explanation

Magnetic field at the centre M due to current through the curved protion DA is
`B _(1) = ( mu _(0) I )/( 4pi R) (( 3pi)/( 2))` inot the plane Magnetic field at the centre M due to current through the straight portion AB is `B _(2) = 0.`
Magnetic field at centre M due to current through the curved protion BC is
`B _(3) = ( mu _(0) I )/( 4pi ( 3 R)) xx (pi)/(2)` into the plane Magnetic field at the centre M due to current through straight portion CD is
`B _(4) = 0`
The resultant magnetic field at M is
`B = B _(1) + B _(2) + B _(3) + B _(4)`
`= ( 3 mu _(0) I )/( 8 R) + 0 + ( mu _(0) I )/( 24 R) + 0 = ( 10)/(24) ( mu _(0) I )/(R)`
`therefore B = 0. 42 ( mu _(0) I )/( R)`