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A 4 A current carrying loop consists of ...

A 4 A current carrying loop consists of three identical quarter circles of radius 5 cm lying in the positive quadrants of the x-y, y-z and z-x planes with their centres at the origin joined together, value of B at the origin is

A

`(mu_(0))/(10)(hati+hatj-hatk)T`

B

`(mu_(0))/(10)(-hati+hatj+hatk)T`

C

`(mu_(0))/(5)(hati+hatj+hatk)T`

D

`10mu_(0)(hati+hatj+hatk)T`

Text Solution

Verified by Experts

The correct Answer is:
D
As `vecB=vecB_(xy)+vecB_(yz)+vecB_(zx)" …(i)"`
where `vecB_("xy")=(mu_(0))/(4pi)(I)/(R) thetahatk, vecB_(yz)=(mu_(0))/(4pi)(I)/(R)thetahati,vecB_(zx)=(mu_(0))/(4pi)(I)/(R)thetahatj,`
Substituting these values in equation (i) we get,
`vecB=(mu_(0))/(4pi)(I)/(R)theta(hati+hatj+hatk)`
Here, `theta=(pi)/(2), I=4A` and R = 5 cm `=5xx10^(-2)m`
`therefore" "vecB=(mu_(0))/(4pi)(I)/(R)theta[hati+hatj+hatk]`
Here, `theta=(pi)/(2), I=4A andR=5 cm=5xx10^(-2)m`
`therefore" "vecB=(mu_(0))/(4pi)xx(4)/(5xx10^(-2))xx(pi)/(2)(hati+hatj+hatk)=10mu_(0)(hati+hatj+hatk)T`
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