The plane of a 5.0 cm x 8.0 cm rectangular loop of wire is parallel to a 0.19-T magnetic field.The loop carries a current of 6.2 A.(a) What torque acts on the loop?(b) What is the magnetic moment of the loop?(c) What is the maximum torque that can be obtained with the same total length of wirecarrying the same current in this magnetic field?
Question
The plane of a 5.0 cm x 8.0 cm rectangular loop of wire is parallel to a 0.19-T magnetic field.The loop carries a current of 6.2 A.(a) What torque acts on the loop?(b) What is the magnetic moment of the loop?(c) What is the maximum torque that can be obtained with the same total length of wirecarrying the same current in this magnetic field?
Solution
(a) The torque (τ) on a current loop in a magnetic field is given by the equation τ = μBsinθ, where μ is the magnetic moment, B is the magnetic field, and θ is the angle between the magnetic field and the normal to the plane of the loop. Since the plane of the loop is parallel to the magnetic field, θ = 0 degrees and sinθ = 0. Therefore, the torque on the loop is 0.
(b) The magnetic moment (μ) of a current loop is given by the equation μ = IAn, where I is the current, A is the area of the loop, and n is the number of turns in the loop. Since the loop is a single turn, n = 1. The area of the loop is A = length x width = 5.0 cm x 8.0 cm = 40 cm^2 = 0.004 m^2. Therefore, the magnetic moment of the loop is μ = IAn = 6.2 A x 0.004 m^2 x 1 = 0.0248 Am^2.
(c) The maximum torque (τ_max) that can be obtained with the same total length of wire carrying the same current in this magnetic field is when the plane of the loop is perpendicular to the magnetic field, i.e., θ = 90 degrees and sinθ = 1. Therefore, τ_max = μB = 0.0248 Am^2 x 0.19 T = 0.004712 Nm.
Similar Questions
A current of 30.0 mA is maintained in a single circular loop of 3.80 m circumference. A magnetic field of 0.510 T is directed parallel to the plane of the loop.(a) Calculate the magnetic moment of the loop. mA · m2(b) What is the magnitude of the torque exerted by the magnetic field on the loop?
Q.32 A rectangular loop of wire of size 4cm x 10cm carries a steady current of 2A. A straight long wirecarrying 5A current is kept near the loop as shown. If the loop and the wire are coplanar, find-(i) the torque acting on the loop and(ii) the magnitude and direction of the force on the loop due to the current carrying wire
A single-turn square loop of wire, 2.00 cm on each edge, carries a clockwise current of 0.250 A. The loop is inside a solenoid, with the plane of the loop perpendicular to the magnetic field of the solenoid. The solenoid has 30.0 turns/cm and carries a clockwise current of 15.0 A.(a) Find the force on each side of the loop.magnitude µNdirection (b) Find the magnitude of the torque acting on the loop. N · m
The figure shows a wire with a loop in it. The current through the wire is 5.00 A and the diameter of the loop is 3.40 cm. What is the magnetic field at the center of the loop?
A circular coil of 25 turns and radius 6.0 cm carrying a current of 10 A, is suspended vertically in a uniform magnetic field of magnitude 1.2 T. The field lines run horizontally in the plane of the coil. Calculate the force and torque on coil due to the magnetic field
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.