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A very long wire ABCDEFBDG is shown in f...

A very long wire ABCDEFBDG is shown in figure carrying current I. AC and CG parts are straight, long and at right angle. At D wire forms a circular turn DEFBD of radius R. AC, CG parts are tangential to circular turn at B and D. Magnetic field at the centre of circle is:

A

`(mu_0 I)/R`

B

`(mu_0I)/(2piR)(pi+1)`

C

`(mu_0I)/(2pi R)(pi + 1/sqrt2 +1)`

D

`(mu _0I)/(2piR) ( pi - 1/ sqrt2)`

Text Solution

Verified by Experts

The correct Answer is:
C
We say we have 3 parts
`B = BA + B_B_+B_C`
`=(mu_0I)/(4 pi R)(sin 90^@ + sin 45^@)+(mu_oI)/(2R)+(mu_0I)/(4 pi R) (sin 45^@ + sin 90^@)` `= (mu_0 I)/(2 piR) ( pi + 1/ sqrt2 +1)`
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