Question

Two parallel straight conductors cross a metre rule at the 2cm and 6cm marks. They carry currents I and 3 I respectively in same direction and produce zero magnetic field at

Answer 1

Given info : Two parallel straight conductors cross a metre rule at the 2cm and 6cm marks. They carry currents 1 A and 3 A respectively in same direction.

To find : the position of point where magnetic field equals to zero.

solution : let A and B are two parallel straight conductor cross a metre rule at the 2cm and 6 cm marks respectively. between them, a point O where magnetic field equals to zero.

let distance from the conductor A to O is r cm

so, distance from the conductor B to O is (6cm - 2cm) - r = (4 - r) cm

magnetic field at point O = 0

⇒magnetic field due to A + magnetic field due to B = 0

⇒μ₀× 1A/2πr - μ₀ × 3A/2π(4 - r) = 0

⇒1/r = 3/(4 - r)

⇒4 - r = 3r

⇒r = 1

Therefore the position of the point where magnetic field becomes zero is (2cm + 1 cm) = 3cm mark on the scale.