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Q.

A current I flows through a lengthy thin walled tube of radius R having a longitudinal slit of width W. The magnetic field inside the tube at the axis under the condition W<<r is (r = distance of a point in the tube from slit)

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a

Zero

b

μ0WI2π2R2r

c

μ0WI4π2Rr

d

μ0WI4π2R2

answer is C.

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Detailed Solution

r = distance of inside point from slit

In the absence of the slit, B = 0 at any inside point.

When the slit is made the remaining part of the pipe will produce some non zero field. This will be equal and opposite to the field produced by slit.

Field B=μ02πr.dI

dI=I2πR(W)B=μ0WI4π2Rr

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A current I flows through a lengthy thin walled tube of radius R having a longitudinal slit of width W. The magnetic field inside the tube at the axis under the condition W<<r is (r = distance of a point in the tube from slit)