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Two circular coils A and B of radius (5)...

Two circular coils `A` and `B` of radius `(5)/sqrt2cm` amd `5cm` respectively current `5amp` and `(5)/sqrt2Amp` respectively The plane of `B` is perpendicular to plane of `A` their centres coincide Find the magnetic field at the centre .

Text Solution

Verified by Experts

The correct Answer is:
`(sqrt5)/(2sqrt2) 4pi xx 10^(-5)T`
`B=sqrt((B_(A)^(2)) + B_(B)^(2))`
`B_(A) = (mu_(0))/(4pi) (2piI_(A))/(r_(A)) = (mu_(0))/(4pi)(2pi xx5)/((5)/sqrt2xx 10^(-2)) =10^(-5) xx 2 sqrt2 pi `
`B_(B) = (mu_(0))/(pi)(2pi xx (5//sqrt2))/(5 xx 10^(-2)) = sqrt2 pi xx10^(-5)`
`B =sqrt(B_(1)^(2) +B_(2)^(2))`
`sqrt((2sqrt2pi xx 10^(-5))^(2) + (sqrt2 pi xx 10^(-5))^(2)`
`B = sqrt5 xx sqrt2 pi xx 10^(-5) = (sqrt5 xx 4pi 10^(-5))/(2sqrt2)T`
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