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CBSE Class 12-science Answered

Write the expression for the magnetic moment begin mathsize 12px style open parentheses straight m with rightwards arrow on top close parentheses end style due to a planar square loop of side 'I' carrying a steady current I in a vector form. In the given figure this loop is placed in a horizontal plane near a long straight conductor carrying a steady current I1 at a distance I as shown. Give reasons to explain that the loop will experience a net force but no torque. Write the expression for this force acting on the loop.
Asked by Topperlearning User | 21 May, 2015, 10:13: AM
answered-by-expert Expert Answer

Magnetic moment due to current carrying loop:

m = I A = I × L × L, here A = area of the square loop = L × L

The net torque on the loop will be zero as , here the angle between vector m and B is zero.

Force experienced by the nearer parallel side of the loop=begin mathsize 11px style fraction numerator straight mu subscript 0 II subscript 1 over denominator 2 πL end fraction left parenthesis attractive right parenthesis end style

Force experienced by the farther parallel side of the loop = begin mathsize 11px style fraction numerator straight mu subscript 0 II subscript 1 over denominator 2 straight pi 2 straight L end fraction left parenthesis repulsive right parenthesis end style

Net force on the loop towards the wire: begin mathsize 11px style fraction numerator straight mu subscript 0 II subscript 1 over denominator 2 πL end fraction minus fraction numerator straight mu subscript 0 II subscript 1 over denominator 2 straight pi 2 straight L end fraction equals fraction numerator straight mu subscript 0 II subscript 1 over denominator 2 straight pi 2 straight L end fraction end style

Answered by | 21 May, 2015, 12:13: PM

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