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Q.

Figure shows a part of an electric circuit. ABCD is a rectangular loop made of uniform wire. The length  AD=BC= 1cm. The sides AB  and DC  are long as compared to the other two sides. The magnetic force per unit length acting on the wire DC  due to the wire AB  if the ammeter reads is  10 A is x×104Nm1. then find the value of  x?
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answer is 5.

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Detailed Solution

By symmetry, each of the wires  and  carries a current of 5A.  As the separation between them is 1cm , the magnetic force per unit length of DC is
  dFdl=μ0i1i22πd=2×107TmA1)(5A)(5A)1×102m=5×104TA=5×104Nm1.
 
 

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