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Q.

A cylindrical wire of radius R is carrying current i uniformly distributed over its cross-section. If a circular loop of radius r is taken as amperian loop, then the variation value of ∮B→. dl→ over this loop with radius r of loop will be best represented by

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a

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b

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c

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d

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answer is B.

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Detailed Solution

Current within radius r < R:

Iin  =  Iπr2 = iπR2πr2  =  ir2R2for r  <  R,  ∮B→. dl→ =μ0Iin = μ0ir2R2 ⇒  Parabolic

for  r  > R,  ∮B→. dl→ =μ0Iin = μ0I ⇒  Constant

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