Depict the magnetic field lines due to two straight, long parallel conductors carrying currents I₁ and I₂ in the same direction. Hence deduce on expression for the force acting per unit length on one conductor due to the other. Is this force attractive or repulsive?
Figure shows a rectangular current carrying loop placed 2 cm away from a long, straight, current carrying conductor. What is the direction and magnitude of the net force acting on the loop?

Solution

Given, two infinitely long conductors AB and CD with currents I₁ and I₂ in same direction respectively, placed parallel to each other, and separated by distance r.

Magnetic field produced by current at any point of CD is $B_{1} = \frac{μ_{o} I_{1}}{2 π r}$

This field acts perpendicular to CD and into the plane of paper. It exerts a force on wire CD carrying current I₂.

Force exerted on unit length of CD is

$F = B_{1} I_{2} I = \frac{μ_{0} I_{1}}{2 πr} \times I_{2} \times 1$

$F = \frac{μ_{0} I_{1} I_{2}}{2 πr} = \frac{μ_{0}}{4 π} . \frac{2 I_{1} I_{2}}{r}$

According to Fleming's left hand rule, this force acts on CD towards AB.

Similarly, conductor CD also exerts an equal force AB towards itself. Hence the two wires get attracted towards each other.

Numerical:

Force on AB, $F_{1} = \frac{μ_{0}}{4 π} . \frac{2 I_{1} I_{2}}{r_{1}} \times length of AB$

Some More Questions From Moving Charges And Magnetism Chapter

Two moving coil meters, M₁ and M₂ have the following particulars:
R₁ = 10 Ω N₁ = 30,
A₁ = 3.6 x 10^–3 m², B₁ = 0.25 T
R₂ = 14 Ω; N₂ = 42,
A₂ = 1.8 x 10^–3 m², B₂ = 0.50 T
(The spring constants k are identical for the two meters).
Determine the ratio of (a) current sensitivity and (b) voltage sensitivity of M₂ and M_1.

For Daily Free Study Material Join wiredfaculty

Moving Charges And Magnetism

Some More Questions From Moving Charges And Magnetism Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction