Question

two infinitely long parallel wires a and b carrying current of 10A and 20A respectively in opposite. direction are placed at a separation of 30 cm. the magnetic field will be zero at

Answer 1

Given:

Two infinitely long parallel wires a and b carrying current of 10A and 20A respectively in opposite. direction are placed at a separation of 30 cm.

To find:

Position where the Magnetic field will be zero?

Calculation:

The required position (point P) will have the field intensity equal and opposite to one another :

$B_{1} = B_{2}$

$\implies \dfrac{ \mu_{0}(2 i_{1} ) }{x} = \dfrac{ \mu_{0}(2 i_{2} ) }{30 + x}$

$\implies \dfrac{ i_{1} }{x} = \dfrac{ i_{2} }{30 + x}$

$\implies \dfrac{ 10 }{x} = \dfrac{ 20}{30 + x}$

$\implies \dfrac{ 1 }{x} = \dfrac{ 2}{30 + x}$

$\implies 30 + x = 2x$

$\implies x = 30 \: cm$

So, point P is 30 cm from 10 Amp wire and 30+30 = 60 cm from 20 Amp wire.