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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 = Bo(2hati + 3hatj + 4hatk)`T, where B0 is constant. The magnitude of flux passing through the square is ______.
Options
`2 B_0 L^2 Wb`
`3 B_0 L^2 Wb`
`4 B_0 L^2 Wb`
`sqrt(29) B_0 L^2 Wb`
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Solution
A square of side L meters lies in the x-y plane in a region, where the magnetic field is given by `B = Bo(2hati + 3hatj + 4hatk)`T, where B0 is constant. The magnitude of flux passing through the square is `underline(4 B_0 L^2 Wb`).
Explanation:
Magnetic flux is defined as the total number of magnetic lines of force passing normally through an area placed in a magnetic field and is equal to the magnetic flux linked with that area.
For elementary area dA of a surface flux linked `dphi = BdA cos theta` or `dphi = vecB*dvecA`
So, Net flux through the surface `phi = oint vecB xx dvecA = BA cos theta`
In this problem, `A = L^2 hatk` and `B = B_0 (2hati + 3hatj + 4hatk)T`
`phi - vecB.vecA = B_0 (2hati + 3hatj + 4hatk) * L^2 hatk = 4B_0L^2 Wb`
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