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...

Thursday, October 1, 2015

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...

The figure is attached
below.

By definition the magnetic field induction $\displaystyle{B}$ of a
current $\displaystyle{I}$ that flows to a straight wire, at distance $\displaystyle{R}$ from the wire
is

$\displaystyle{B}=\mu\cdot\frac{{I}}{{{2}\cdot\pi\cdot{R}}}$

where
$\displaystyle\mu$ 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.

$\displaystyle{B}_{{1}}={B}_{{2}}$
rArr mu*I_1/(2*pi*R_1) =mu*I_2/(2*pi*R_2)

$\displaystyle\frac{{R}_{{1}}}{{R}_{{2}}}$
=I_1/I_2 rArr R_2 =3R_1

with the condition $\displaystyle{R}_{{1}}+{R}_{{2}}=$
6-2 =4 cm

$\displaystyle{R}_{{1}}+{3}\cdot{R}_{{1}}={4}$

$\displaystyle{4}{R}_{{1}}={4}\Rightarrow{R}_{{1}}={1}{c}{m}$

Thus
the field will be zero at $\displaystyle{R}_{{1}}={1}{c}{m}$ 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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Help Notes

Thursday, October 1, 2015