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A long thin walled pipe of radius R carr...

A long thin walled pipe of radius `R` carries a current I along its length The current density is uniform over the circumference of the pipe The magnetic field at the center of the pipe due to quarter portion of the pipe shown, is
.

A

`(mu_(0)Isqrt2)/(4pi^(2)R)`

B

`(mu_(0)I)/(pi^(2)R)`

C

`(2mu_(0)Isqrt2)/(pi^(2)R)`

D

None

Text Solution

Verified by Experts

The correct Answer is:
A
`dI = (I)/(2pi) dtheta`
Field at center due to very long wire carrying current dI
`dB = (mu_(0))/(2pi) = (I)/(R) = (mu_(0))/(4pi^(2)) (I)/(R)dtheta`
`oversetrarr(B) = intdoversetrarrB=[underset(0)overset(pi//2)intdBcos theta hati + underset(0)overset(pi//20i)intdB sin thetahati]`
`= (mu_(0))/(4 pi^(2)R)(I)/(R)[underset(0)overset(pi//2)intcos 0 dtheta hati + underset(0)overset(pi//20i)int sin0 d thetahatj]`
`oversetrarr(B) = (mu_(0))/(4pi^(2)R) (I)/(R)[hati +hatj]impliesB=(mu_(0))/(4pi^(2)R) (I)/(R) sqrt2`
.
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