Question

Two long parallel wires P and Q are held perpendicular to the plane of the paper at a separation of 5 m. If P & Q carry currents of 2.5 A & 5A respectively in the same direction, then what is magnetic field at a point mid- way between P and Q?

Answer 1

Mangetic field B due to a current carrying conductor at a distance d from it is given by 
       =  Mu I / 2π d                I = current      Mu = permeability in the medium (vacuum)

Suppose P is to the left of Q.  Midpoint is at  d = 5/2 m = 2.5 m

If we take the wire P, direction of B due to P at midpoint between wires is upwards on the plane of paper.  I assume that the current is coming out of plane of paper. Its strength is

B = 4 π * 10^-7 * 2.5 / 2 * π * 2.5  =  2 * 10^-7 Tesla,  upwards

If we take the wire Q, direction of B due to Q will be downwards on the plane of paper.

B = 4 π * 10^-7 * 5 / 2 * π * 2.5  =  4 * 10^-7 Tesla,  downwards

Resultant Magnetic field is :  4 * 10^-7 downwards

Answer 2

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