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
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
OPPS! Plz take care that the scale is CENTIMETER.