Question

Figure shows two long straight wires lying along X and Y axes, well insulated from each other and carrying a current i. If AB and CD are a pair of lines
equally inclined to the axes, then the magnetic field is zero on the line/lines.​

Answer 1

Answer:

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Answer 2

The net magnetic field will be Zero at line AB

GIVEN

• 2 straight wires along X-axis and Y-axis.
• AB & CD are line segments equally inclined to the axis.

TO FIND

Which line has zero magnetic field?

SOLUTION

We can simply solve the above problem as follows-

We know that Magnetic field due to a current carrying wire is given by the expression -

$B = \frac{μ₀i }{2\pi d}$

Where,

d = perpendicular distance of the point from the wire.

Let, The magnetic field due the wire along x-axis be, B₁

The magnetic field due to the wire along y-axis be, B₂

$B₁ = \frac{μ₀i }{2\pi d₁}$

And,

$B₂ = \frac{μ₀i }{2\pi d₂}$

Since, the lines AB and CD are equally inclined, OX = d₁ = d₂

According to Right Hand thumb rule -

B₁ and B₂ are equal in magnitude and opposite in direction

so,

At ,

AB = B₁ + B₂

=

$= \frac{μ₀i }{2\pi d₁} - \frac{μ₀i }{2\pi d₂}$

= 0

Hence, The net magnetic field will be Zero at line AB

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