Questions
Two parallel wires P and Q placed at a separation carry electric currents and in opposite directions as shown in figure. Find the point on the line PQ (in cm) where the resultant magnetic field is zero.
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
and will be directed downward in the plane of the figure.
The field at the same point due to the current i2 will be
directed upward in the plane of the figure.
If the resultant field at R is zero, we should have
giving,
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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
and will be directed downward in the plane of the figure.
The field at the same point due to the current i2 will be
directed upward in the plane of the figure.
If the resultant field at R is zero, we should have
giving,
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