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Shown in the figure is a conductor carry...

Shown in the figure is a conductor carrying a current I. The magnetic field intensity at the point O(common centre of all the three arcs) is :

A

`(5mu_(0)I theta)/(24pi r)`

B

`(mu_(0) I theta)/(24pir )`

C

`(11mu_(0)I theta)/(24pi r)`

D

zero

Text Solution

Verified by Experts

The correct Answer is:
A
Hint : Find B due to each arc at O and add them using vector addition.
Since magnetic field at the centre of an arc is equal to `B=(mu_(0)I)/(4pi r) theta`
hence, net `B=(mu_(0)I)/(4pi) [(1)/(r ) -(1)/(2r ) +(1)/(3r)] theta =(5mu_(0)I theta)/(24pir )`
`=3.9 xx 10^(-5) T`.
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