Practice Questions

Summarize the nature of the force between two long, parallel current-carrying conductors. State whether parallel currents and antiparallel currents attract or repel each other.

Evaluate the common idealization that 'a long solenoid produces a perfectly uniform magnetic field inside and zero field outside'.

Name the SI unit of magnetic field and define it.

Justify the use of a soft iron core within the coil of a moving coil galvanometer.

Apply the right-hand rule to determine the direction of the magnetic field at the center of a circular loop carrying current in a clockwise direction.

Explain the key observation made by Hans Christian Oersted in 1820 that established a link between electricity and magnetism.

Define a solenoid.

A straight conductor of length $25$ cm is placed in a uniform magnetic field of $0.4$ T. It carries a current of $10$ A. Calculate the magnitude of the magnetic force on the conductor when it is oriented at an angle of $60^{\circ}$ with respect to the magnetic field.

Define the Lorentz force acting on a charge $q$ moving with velocity $\mathbf{v}$ in the presence of an electric field $\mathbf{E}$ and a magnetic field $\mathbf{B}$.

A circular coil has $50$ turns and a radius of $5.0$ cm. It carries a current of $2.0$ A. Calculate the magnitude of the magnetic field at its center. Use $\mu_0 = 4\pi \times 10^{-7} \text{ T·m/A}$.

A long, straight wire carries a steady current of $40$ A. Apply Ampere's circuital law to calculate the magnitude of the magnetic field at a perpendicular distance of $10$ cm from the wire.

Two long, parallel straight wires are placed $5$ cm apart in a vacuum. Wire 1 carries a current of $10$ A and Wire 2 carries a current of $15$ A, both in the same direction. Calculate the magnitude of the force per unit length on Wire 2 and determine if the force is attractive or repulsive.

A solenoid is $1.0$ m long and has an inner diameter of $4.0$ cm. It has 4 layers of windings with $500$ turns per layer. If it carries a current of $5.0$ A, calculate the magnitude of the magnetic field inside the solenoid near its center.

A student proposes that a stationary electron can be accelerated using only a uniform magnetic field. Critique this proposal, explaining its feasibility based on the Lorentz force.

Justify the statement: 'The magnetic force acting on a moving charged particle does no work and cannot change its kinetic energy.'

Design a moving coil galvanometer with very high current sensitivity. Propose four specific modifications to its construction and justify how each modification enhances sensitivity.

A circular loop and a square loop are constructed from the same length of conducting wire, $L$, and carry the same current, $I$. They are placed in the same uniform magnetic field, $\mathbf{B}$. Justify which loop will experience a greater maximum torque.

A classmate claims that Ampere's Circuital Law, $\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_{enc}$, is always the most efficient method to calculate the magnetic field for any current distribution. Critique this claim.

Formulate the mathematical expression for the force per unit length between two infinitely long, straight, parallel conductors. Using this, propose a precise, modern definition for the SI unit of current, the Ampere.

Describe the path of a charged particle that enters a uniform magnetic field if its initial velocity is (a) perpendicular to the magnetic field, and (b) at an arbitrary angle to the magnetic field. Recall the formula for the radius of the circular path.

State Ampere's circuital law and explain the right-hand rule used to determine the sign of the current.

Recall the expression for the magnetic field inside a long solenoid. Calculate the magnitude of the magnetic field inside a solenoid of length $0.5$ m, having 500 turns and carrying a current of $5$ A.

Define the magnetic moment of a current loop carrying current $I$ with area vector $\mathbf{A}$.

Describe the basic principle of a moving coil galvanometer. Recall the expression that relates the coil's deflection to the current flowing through it.

An alpha particle (charge $q = +3.2 \times 10^{-19}$ C, mass $m = 6.64 \times 10^{-27}$ kg) moves in a circular path of radius $15$ cm in a uniform magnetic field of $0.8$ T. Calculate the speed of the alpha particle and its frequency of revolution.

Analyze the trajectory of a charged particle that enters a uniform magnetic field with its velocity vector at an angle $\theta$ (where $0 < \theta < 90^{\circ}$) to the field direction. Explain why the path is helical.

Examine the Biot-Savart Law, $d\mathbf{B} = \frac{\mu_0}{4\pi} \frac{I d\mathbf{l} \times \mathbf{r}}{r^3}$. Along which line relative to the current element $I d\mathbf{l}$ is the magnetic field guaranteed to be zero?

Propose a configuration of uniform electric and magnetic fields, known as a velocity selector, that will allow a positively charged particle to pass through undeflected only if it has a specific velocity $\mathbf{v}$. Derive the condition for this specific velocity.

A researcher proposes to create a magnetically shielded room for sensitive experiments by enclosing it within a large, current-carrying solenoid. Critique the effectiveness of this design.

Identify the vector expression for the torque $\mathbf{\tau}$ experienced by a current loop with magnetic moment $\mathbf{m}$ placed in a uniform external magnetic field $\mathbf{B}$.

Recall the formula for the magnetic field at the center of a circular coil with $N$ turns, radius $R$, carrying a current $I$. Calculate the magnitude of the magnetic field at the center of a 100-turn coil of radius $8.0$ cm carrying a current of $0.40$ A.

State the Biot-Savart law in its vector form for the magnetic field $\mathrm{d}\mathbf{B}$ produced by a current element $I \mathrm{d}\mathbf{l}$ at a position vector $\mathbf{r}$ from the element.

List three fundamental properties of the magnetic force on a charged particle moving in a magnetic field.

You are given a galvanometer with internal resistance $R_G = 50.0 \text{ } \Omega$ that shows a full-scale deflection for a current of $I_g = 1.00 \text{ mA}$. Design an ammeter capable of measuring currents up to $1.00 \text{ A}$. Create a circuit diagram and calculate the required shunt resistance.

A rectangular loop of dimensions $10$ cm by $5$ cm carries a current of $5$ A. A uniform magnetic field of magnitude $0.2$ T is directed parallel to the longer side of the loop. Calculate the magnitude of the torque acting on the loop.

An electron with a velocity of $\mathbf{v} = (2.0 \times 10^6 \hat{\mathbf{i}} + 3.0 \times 10^6 \hat{\mathbf{j}})$ m/s enters a region with a uniform magnetic field $\mathbf{B} = 0.05 \hat{\mathbf{i}}$ T. Calculate the magnetic force acting on the electron. (Charge of electron $q = -1.6 \times 10^{-19}$ C)

Formulate an experimental procedure to determine the charge-to-mass ratio ($q/m$) of an electron. Derive the necessary mathematical expression and describe the required setup.

Explain how a moving coil galvanometer can be converted into (a) an ammeter and (b) a voltmeter.

A galvanometer with a coil resistance of $15 \Omega$ shows a full-scale deflection for a current of $4$ mA. Demonstrate how you would convert this galvanometer into an ammeter of range $0-6$ A and calculate the required shunt resistance.

Create a numerical problem to find the magnetic field at the center of a semi-circular arc. A long straight wire carrying a current of $I = 10 \text{ A}$ is bent into a shape consisting of two straight sections and a semi-circular arc of radius $R = 5.0 \text{ cm}$, as shown in the figure for Example 4.5(a) in the source text. Formulate and solve the problem.

Examine the reason for using a cylindrical soft iron core in a moving coil galvanometer.

Two long parallel wires carry steady currents in the same direction. Evaluate the nature of the force between them. Propose what would happen if one wire carried a steady DC current and the other carried a sinusoidal AC current.

Compare and contrast the Biot-Savart law for magnetism with Coulomb's law for electrostatics. List two similarities and two differences.

Design an experiment to verify the inverse relationship between the magnetic field ($B$) around a long straight conductor and the distance ($r$) from it. Justify your choice of measuring instruments and procedure to ensure accuracy.

A proton enters a region of uniform magnetic field with a certain velocity and moves in a circle. An alpha particle enters the same magnetic field with the same velocity. Analyze the ratio of the radii of their circular paths ($r_p / r_{\alpha}$). Assume mass of alpha particle is 4 times mass of proton, and charge is 2 times.