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Chapter 16: Problem 13

A magnetic needle is kept in a non-uniform magnetic field. It experiences (A) A force and torque (B) A force but not a torque (C) A torque but not a force (D) Neither a force nor a torque

Short Answer

Expert verified
The magnetic needle in the non-uniform magnetic field experiences a torque but not a force. This is because the magnetic force acting on the needle depends on its velocity, which is zero if it's stationary, and the magnetic torque is due to the misalignment of the magnetic field with the needle's magnetic moment. Thus, the correct answer is (C) A torque but not a force.

Step by step solution

01

Understand the magnetic force on the needle

First, let's recall that the magnetic force acting on a magnetic object (like our needle) is given by the equation: \(F = q(v \times B)\), where 'q' is the charge, 'v' is the velocity of the charge, and 'B' is the magnetic field. If the needle is stationary and not moving, the velocity 'v' will be zero, thus the magnetic force acting on the needle will be zero.
02

Understand the magnetic torque on the needle

Now, let's consider the magnetic torque. The torque acting on a magnetic object in a magnetic field is given by the equation: \(\tau = m \times B\), where 'm' is the magnetic moment of the object, and 'B' is the magnetic field. Since the needle is in a non-uniform magnetic field, the magnetic field will have different directions and magnitudes at different points. It means the needle will experience a magnetic torque due to misalignment of the magnetic field with the needle's magnetic moment.
03

Choose the correct option

From our analysis in Step 1 and Step 2, we can conclude that the magnetic needle experiences a torque but not a force since it's in a non-uniform magnetic field and not moving. Therefore, the correct choice is (C) A torque but not a force.

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