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Two parallel wires P  and Q  placed at a separation d=6cm  carry electric currents  i1=5A and i2=2A  in opposite directions as shown in figure. Find the point on the line PQ  (in cm) where the resultant magnetic field is zero.

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detailed solution

Correct option is D

At the desired point, the magnetic fields due to the two wires must have equal magnitude  but opposite directions. The point should be either to the left of P  or to the right of Q. As the wire  Q has smaller current, the point should be closer to Q . Let this point R be at a distance x from Q.
The magnetic field at R due to the current  i1 will have magnitude B1=μ0i12π(d+x)  

and will be directed downward in the plane of the figure. 

The field at the same point due to the current i2   will be B2=μ0i22πx
directed upward in the plane of the figure. 

If the resultant field at R is zero, we should have

B1=B2, so that i1d+x=i2x
giving,    

x=i2di1i2=(2A)(6cm) (3A)=4cm
 

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detailed solution

Correct answer is 4

At the desired point, the magnetic fields due to the two wires must have equal magnitude  but opposite directions. The point should be either to the left of P  or to the right of Q. As the wire  Q has smaller current, the point should be closer to Q . Let this point R be at a distance x from Q.
The magnetic field at R due to the current  i1 will have magnitude B1=μ0i12π(d+x)  

and will be directed downward in the plane of the figure. 

The field at the same point due to the current i2   will be B2=μ0i22πx
directed upward in the plane of the figure. 

If the resultant field at R is zero, we should have

B1=B2, so that i1d+x=i2x
giving,    

x=i2di1i2=(2A)(6cm) (3A)=4cm
 

Talk to our academic expert!

+91

Are you a Sri Chaitanya student?

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