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Q.

A wire is bent into the shape shown in figure (a), and the magnetic field is measured at P1 when the current in the wire is I . The same wire is then formed into the shape shown In figure (b), and !he magnetic field measured at point P2, when the current Is again I . If the total length of wire is the same in each case? what is B1 & B2.

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a

B1=μ0I4πl212

b

B1=μ0I4πl2+12

c

B2=πμ0I4l

d

B2=πμ0I16l

answer is A, B.

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Detailed Solution

For the figure (a), we have

B12=B56=0

B23=μ0I4πlsin(0)+sinπ4

B45=B23=μ0I42πl

B34=μ0I4πlsinπ4+sinπ4

B1=μ0I4πl2+12

For figure (b), we observe that if r is the radius of the semicircle, then

 

B2=μ0I4r=μ0I44lπ=πμ0I16l

 

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