ON A METER SCALE , TWO LONG PARALLEL CONDUCTORS AT RIGHT ANGLE TO IT PLACED AT 2cm & 6cm. THEY CARRY CURRENTS OF 1A & 3A RESPECTIVELON A METER SCALE , TWO LONG PARALLEL CONDUCTORS AT RIGHT...

ON A METER SCALE , TWO LONG PARALLEL CONDUCTORS AT RIGHT ANGLE TO IT PLACED AT 2cm & 6cm. THEY CARRY CURRENTS OF 1A & 3A RESPECTIVEL

ON A METER SCALE , TWO LONG PARALLEL CONDUCTORS AT RIGHT ANGLE TO IT PLACED AT 2cm & 6cm. THEY CARRY CURRENTS OF 1A & 3A RESPECTIVELY IN SAME DIRECTION. THEY WILL PRODUCE ZERO MAGNETIC FIELD AT THE

 

A) 0cm           B)10cm      C)3cm            D)6cm

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valentin68 | College Teacher | (Level 3) Associate Educator

Posted on

The figure is attached below.

By definition the magnetic field induction `B`  of a current `I`  that flows to a straight wire, at distance `R` from the wire is

`B = mu*I/(2*pi*R)`

where `mu` is the magnetic permeability of the medium.

Because the currents are parallel and in the same direction the condition of having zero magnetic field happens is a point between the two wires where the field of one wire enters the page and the other exits the page.

`B_1 =B_2 rArr mu*I_1/(2*pi*R_1) =mu*I_2/(2*pi*R_2)`

`R_1/R_2 =I_1/I_2 rArr R_2 =3R_1`

with the condition `R_1 +R_2 = 6-2 =4 cm`

`R_1 +3*R_1 =4`

`4R_1 =4 rArr R_1 =1cm`

Thus the field will be zero at `R_1 =1 cm` distance to the right of first wire. This means that on the cm scale this point will be at the 3 cm mark.

The correct answer is C) 3 cm

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