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Question

Two concentric coils each of radius equal to 2π cm are placed in such a manner that their planes are at right angles to each other. Current of 3 A and 4 A respectively are flowing through the coil. What will be the magnetic induction at the center of the loop ?

A
5×105 T
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B
7×105 T
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C
1×105 T
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D
None of these
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Solution

The correct option is A 5×105 T

The direction of the magnetic fields due to both the loops is determined by using right-hand thumb rule.

Magnetic field due to a loop-B carrying current 4 A is,

B1=μ0I2R

B1=4π×107×42×2π×102

B1=4×105 T along yaxis

So, magnetic field due to loop-A carrying current 3 A is,

B2=μ0I2R

B2=4π×107×32×2π×102

B2=3×105 T along xaxis

So the net magnetic field is given by,

Bnet=B1+B2=B1 ^j+B2 ^i

Bnet=|B1|2+|B2|2

Bnet=(4×105)2+(3×105)2

Bnet=5×105 T

Hence, option (a) is correct.

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