A conductor carrying current I is of the type as shown in figure. Find the magnetic field induction at the common centre O of all the three arcs.

Options

A. `(5mu_(0)Itheta)/(24pir)`
B. `(mu_(0)Itheta)/(24pir)`
C. `(11mu_(0)Itheta)/(24pir)`
D. zero

Answer

A

Explanation

`B = B_(1)-B_(2) + B_(3)`
`= (mu_(0)Itheta)/(4pir)-(mu_(0)Itheta)/(8pir) + (mu_(0)Itheta)/(12pir)`
`= (mu_(0)Itheta)/(4pir) (1-(1)/(2) + (1)/(3))`
`= (mu_(0)Itheta)/(4pir)((6-3+2)/(6))`
`= (mu_(0)Itheta)/(4pir) xx (5)/(6)`