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Two very long wires carrying equal curre...

Two very long wires carrying equal current i are bent and arranged as shown in figure. Both AB and CD are arcs of the same circle, both subtending right angles at the centre O. The magnetic field at O is:

A

a.`(mu_(0)i)/(4pi R)`

B

b.`(mu_(0)i)/(4pi R)sqrt2`

C

c.`(mu_(0)i)/(2pi R)`

D

d.`(mu_(0)i)/(2pi R) (pi + 1)`

Text Solution

Verified by Experts

The correct Answer is:
C
Magnetic induction due to AA´ and BB´ is given as `B_(1) = (mu_(0)i)/(4pi R)`
Magnetic induction due to CC´ and DD´ is zero at O.
Magnetic indication due to BA is given as `B_(2)= (mu_(0)i)/(8R)`
Magnetic induction due to CD is given as `B_(3) = (-mu_(0)i)/(8R)`
Thus net magnetic induction at O is given as `B_(0) = 2B_(1) + B_(2) + B_(3), B_(0) = (mu_(0)i)/(2pi R)`
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