Q.

A long straight wire carrying current I1 is placed in the plane of a ribbon carrying current I2 parallel to the wire. The width of ribbon is b. The straight conductor is placed at a distance a from the nearer edge of ribbon. Find the force of attraction per unit length between the two.

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a

μ0I1I22π  log  a+ba

b

μ0I1I22π  log  aa+b

c

μ0I1I22π  log  ab

d

μ0I1I22π  log  a+ba

answer is A.

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Detailed Solution

Consider an elementary strip of width dx on the sheet at a distance x from the wire.Force on this element is, dF=μ0I12πx  I2dxTotal force on unit length of sheet isF= ∫aa+b  μ0I12πx I2dx F=μ0I1I22π∫aa+b  1x dx =μ0I1I22π  log a+bb
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A long straight wire carrying current I1 is placed in the plane of a ribbon carrying current I2 parallel to the wire. The width of ribbon is b. The straight conductor is placed at a distance a from the nearer edge of ribbon. Find the force of attraction per unit length between the two.