Q.

Figure shows variation of magnetic field inside and outside two cylindrical wires P and Q carrying currents that are uniformly distributed across the cross-section of wires. If current density for two wires are jP and jQ, then

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a

jP<jQ

b

jP=jQ

c

iQ may be >iP

d

jP>jQ

answer is C, D.

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Detailed Solution

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At the surface of a current-carrying wire,
B=12μ0Jr JBr
 as slope of wire P > slope of wire Q, therefore jP>jQ

From the graph, rP<rQ

iQ=jQ×πrQ2

iP=jP×πrP2

If jPrP2>jQrQ2, then iP>iQ

If jPrP2<jQrQ2, then iP<iQ

If jPrP2=jQrQ2, then iP=iQ

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