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Q.

The current density in a wire of radius R varies with radial distance r as j=λr2, where λ is a constant
I. Total current passing through the cross-section of wire is πλR42  
II. The field at distance r > R is μ0λR44r 
III. The field at distance r < R is μ0λr34

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a

II, III

b

I, III

c

I, II, III

d

I, II

answer is D.

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Detailed Solution

Question Image 
dI=j2πrdr
I=2πk0rr2dr=2πkr33
B2πr=μ0I=μ02πkr33
B=μ0kr23
r<R
B2πr=μ02πλ0rr3dr=μ02πλr44
B=μ0λr34

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