Practice Questions

Calculate the torque experienced by a short bar magnet with a magnetic moment of $0.40 \text{ J T}^{-1}$ when it is placed in a uniform magnetic field of $0.16 \text{ T}$, with its axis making an angle of $60^{\circ}$ with the field.

State Gauss's law for magnetism and write its mathematical expression.

Define magnetic susceptibility, represented by the symbol $\chi$.

List any three fundamental properties of magnetic field lines.

A closely wound solenoid has $1000$ turns and an area of cross-section of $2.0 \times 10^{-4} \text{ m}^2$. It carries a current of $4.0 \text{ A}$. Calculate its associated magnetic moment.

Evaluate the claim that a current-carrying toroid is an ideal example of a magnetic configuration that lacks distinct north and south poles.

Name the physical quantity that is defined as the net magnetic moment per unit volume of a material.

Analyze what happens to the magnetic poles if a straight bar magnet is bent into a U-shape.

A long solenoid has $1000$ turns per metre and carries a current of $2.5$ A. Calculate the magnetic intensity ($H$) inside the solenoid.

Justify why soft iron is preferred for making cores of electromagnets, while steel is preferred for making permanent magnets, by evaluating their respective magnetic properties like retentivity and coercivity.

Recall the expression for the magnetic potential energy $U_m$ of a magnetic dipole in a uniform magnetic field $\mathbf{B}$. Identify the orientations for the most stable and most unstable equilibrium.

Summarize the key differences between electrostatic field lines and magnetic field lines regarding their origin and path.

Compare the behavior of diamagnetic and paramagnetic substances when placed in an external non-uniform magnetic field. Contrast their magnetic susceptibility values.

Apply the concept of magnetic susceptibility to classify a material for which $\chi = -1.0$.

Explain why magnetic monopoles are not known to exist, based on the behavior of a bar magnet when it is broken.

Recall the formula for the torque experienced by a magnetic dipole in a uniform magnetic field. Explain each term in the vector equation.

What is the value of magnetic susceptibility ($\chi$) for a perfect diamagnet, such as a superconductor?

A short bar magnet has a magnetic moment of $0.5 \text{ J T}^{-1}$. Recall the formula and calculate the magnitude of the magnetic field on its axis at a distance of $10$ cm from its center. (Use $\frac{\mu_0}{4\pi} = 10^{-7} \text{ T m A}^{-1}$).

Explain the phenomenon of diamagnetism and describe how a diamagnetic material behaves in an external magnetic field.

Critique the depiction of magnetic field lines for a finite solenoid as being 'completely straight and confined' within the solenoid and abruptly ending at the edges. Propose corrections to make the diagram physically accurate.

Formulate an expression for the work done by an external agent in rotating a magnetic dipole of moment $\mathbf{m}$ from its stable equilibrium position to its unstable equilibrium position in a uniform magnetic field $\mathbf{B}$.

Compare and contrast magnetism with electrostatics by creating a table that shows the electrostatic analog for key magnetic quantities and laws.

Critique the statement: 'Magnetic field lines represent the lines of force on a moving charged particle at every point.' Justify your critique.

Evaluate the analogy between an electric dipole and a magnetic dipole. Your evaluation should highlight one key similarity in their far-field behavior and one fundamental difference concerning the nature of their field lines.

A bar magnet of magnetic moment $m = 0.5 \text{ J T}^{-1}$ is in a uniform magnetic field of $0.2 \text{ T}$. Calculate the magnetic potential energy of the magnet when its axis is aligned (a) parallel to the field (stable equilibrium) and (b) anti-parallel to the field (unstable equilibrium).

A bar magnet with a magnetic moment of $2.0 \text{ J T}^{-1}$ is aligned with a uniform magnetic field of $0.25 \text{ T}$. Calculate the work done by an external agent to rotate the magnet from its most stable position to its most unstable position.

Justify why magnetic monopoles are considered non-existent, using Gauss's law for magnetism and the behavior of a bar magnet when broken.

Propose a method to determine which of two identical-looking iron bars, A and B, is a magnet, using nothing but the two bars themselves. Justify why your method works.

Justify the statement: 'Diamagnetism is a universal property present in all materials, but it is often masked.'

Design an experiment to distinguish between a paramagnetic and a diamagnetic liquid. Your design should specify the apparatus needed and the expected observations that would justify your conclusion.

Design a simple electromagnet using a solenoid and a soft iron core. Justify your choice of a soft iron core by evaluating its magnetic properties in this application.

Analyze why the magnetic field lines of a bar magnet form continuous closed loops, while the electric field lines of an electric dipole do not.

A short bar magnet has a magnetic moment of $0.64 \text{ J T}^{-1}$. Calculate the magnitude of the magnetic field produced by the magnet at a distance of $20 \text{ cm}$ from its center on (a) its axial line and (b) its equatorial line.

Apply Gauss's law for magnetism to analyze why magnetic monopoles are considered non-existent.

Describe the classification of materials into diamagnetic, paramagnetic, and ferromagnetic based on their magnetic susceptibility ($\chi$) and relative magnetic permeability ($\mu_r$).

Explain the concept of a bar magnet being an equivalent solenoid. Describe how the magnetic field lines of both are similar.

Formulate a hypothesis to explain the Meissner effect in superconductors, treating it as an extreme case of a known magnetic property.

Analyze the validity of the statement: 'Every magnetic field configuration must have a north pole and a south pole.' Use the magnetic field of a toroid as a counterexample.

A student claims that configuration $PQ_6$ in the provided text's Figure 5.4 is the most stable among all shown configurations. Evaluate this claim and justify it using the concept of potential energy $U_m = -\mathbf{m} \cdot \mathbf{B}$.

A solenoid with $500$ turns per metre carries a current of $3 \text{ A}$. It is filled with a magnetic material having a relative magnetic permeability of $200$. Calculate (a) the magnetic intensity $H$, (b) the magnetisation $M$, and (c) the magnetic field $B$ inside the core.

Define magnetic intensity, represented by the symbol $\mathbf{H}$.

Propose a modification to Gauss's law of magnetism if magnetic monopoles with magnetic charge $q_m$ were discovered.

Examine the properties that differentiate soft ferromagnetic materials from hard ferromagnetic materials. Apply this knowledge to suggest a suitable material for the core of an electromagnet and for a permanent magnet, justifying your choices.

You are given two identical iron bars, A and B. One is magnetised, but you do not know which. Demonstrate a method to identify the magnet using only the two bars.

Design an experiment to determine the magnetic moment $m$ of a short bar magnet. Assume you are provided with a compass magnetometer and access to the Earth's horizontal magnetic field $B_H$.