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Question

A square of side L meters lies in the x-y plane in a region where the magnetic field is given by ¯B=B0(2^i+3^j+4^k)T,where B0 is constant. The magnitude of flux passing through the square is:

A
8B0L2Wb
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B
12B0L2Wb
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C
4B0L2Wb
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D
4×29B0Wb
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Solution

The correct option is C 4B0L2Wb
Area vector =A=L2^k ...(Perpendicular to x-y plane)

Magnetic field vector,B=B0(2^i+3^j+4^k)T
ϕ=B.A

ϕ=B0(2^i+3^j+4^k).L2^k

ϕ=B0(2L2^i.^k+3L2^j.^k+4L2^k.^k)

^i.^k=0 & ^j.^k=0 & ^k.^k=1

ϕ=B04L2

ϕ=4B0L2wb

where L= length of side of square

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