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Q.

Three wires are carrying same constant current I in different directions. Four loops enclosing the wires in different manners are shown in the figure. The direction of dl is shown in the figure.

Question Image

Then, match the Column I with Column II and select the correct option from the codes given below,

 COLUMN – I  COLUMN – II 
A)Along closed loop 1P)B.dl=μ0I
B)Along closed loop 2Q)B.dl=μ0I
C)Along closed loop 3R)B.dl=0
D)Along closed loop 4S)net work done by the magnetic force to move a unit charge along the loop is zero
  T)B.dl=μ0(2I) 

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a

Aq,s;Bp,s;Cr,s;Dr,s

b

Ap,q;Bp,s;Cq,s;Dp,r,s

c

Ap,s;Bs,q,r;Cp,q,r;Dp,q

d

Ap,q;Bs,r;Cp,r;Dp,q,s

answer is A.

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Detailed Solution

Work done by magnetic field on the charge = 0 in any part of its motion ‘s’ is matching for all parts (i), (ii), (iii), (iv) 
For loop 1, 
Σlin=i+ii=i

      B.dI=μ0i

For loop 2,  Σlin=ii+i=i
        B.dI=μ0i
For loop  3,    Σlin=i+i=0
        B.dI=0
For loop 4,  Σlin=+ii=0
           B.dI=0

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