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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_0I)/R`

B

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

C

`(mu_0I)/(2piR)(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 = B_(A) +B_(E) +B_(C)`
`=(mu_(0)I)/(4piR)(sin90^@+sin45^@)ox +(mu_(0)I)/(2R) ox + (mu_0 I)/(4pi R) (sin 45^@ + sin 90^@)ox`
`=(mu_0I)/(2piR) (pi + 1/(sqrt2) +1)`
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