CBSE Class 12 · 2020 · Magnetic Effects of CurrentShort Answer

Two long straight parallel wires A and B separated by a distance

d

carry equal currents

I

flowing in the same direction.
(a) Find the magnetic field at a point P situated between them at a distance

x

from one wire.
(b) Show graphically the variation of the magnetic field with distance

x

for

0 < x < d

Solution

At P the two wires produce fields in opposite directions (currents are parallel), so they subtract:

B_{P} = \frac{μ _{0} I}{2 π x} - \frac{μ _{0} I}{2 π ( d - x )} = \frac{μ _{0} I ( d - 2 x )}{2 π x ( d - x )} .

(b)

B_{P}

is large and positive near wire A (

x \to 0

), falls to zero at the midpoint

x = \frac{d}{2}

, then reverses sign and grows in magnitude towards wire B (

x \to d

). The graph crosses zero at

x = d /2

and diverges at both ends.

CBSE Class 12 Board · 2020 · Subjective