Magnetism: NMAT Physics Review

Magnetism is a fundamental topic in physics and a recurring subject in the NMAT Physics section. Questions related to magnetic forces, magnetic fields, electromagnetic induction, and the behavior of charged particles in magnetic fields often test both conceptual understanding and problem-solving skills. This comprehensive review is designed to help NMAT examinees build a strong foundation in magnetism, connect formulas with physical meaning, and approach exam questions with confidence.

Introduction to Magnetism

Magnetism arises from the motion of electric charges and is one of the four fundamental forces of nature. In everyday life, magnetism is observed in bar magnets, compasses, electric motors, and generators. At the microscopic level, magnetism originates from the orbital motion and spin of electrons inside atoms.

Magnetic effects are closely linked to electricity, and together they form the field of electromagnetism. Understanding magnetism requires familiarity with magnetic poles, magnetic fields, and how magnetic forces interact with moving charges and current-carrying conductors.

Magnetic Poles and Magnetic Materials

Every magnet has two poles: a north pole and a south pole. Like poles repel each other, while unlike poles attract. Magnetic poles always exist in pairs; isolating a single magnetic pole (a magnetic monopole) has not been observed in classical physics.

Materials respond differently to magnetic fields and are classified as:

• Ferromagnetic materials – strongly attracted to magnets (e.g., iron, cobalt, nickel)
• Paramagnetic materials – weakly attracted to magnets
• Diamagnetic materials – weakly repelled by magnets

Ferromagnetic materials can be permanently magnetized due to the alignment of magnetic domains within the material.

Magnetic Field and Magnetic Field Lines

A magnetic field is a region around a magnet or current-carrying conductor where magnetic forces can be detected. It is represented by the symbol B and is measured in tesla (T).

Magnetic field lines are imaginary lines used to visualize magnetic fields. They have the following properties:

• They emerge from the north pole and enter the south pole outside the magnet
• They form closed loops
• The closer the lines, the stronger the magnetic field
• They never intersect

For a bar magnet, the magnetic field is strongest near the poles.

Magnetic Force on Moving Charges

A charged particle moving in a magnetic field experiences a magnetic force given by:

F = qvB sinθ

where q is the charge, v is the velocity of the particle, B is the magnetic field strength, and θ is the angle between the velocity vector and the magnetic field.

Important characteristics of magnetic force include:

• The force is always perpendicular to both velocity and magnetic field
• No work is done by the magnetic force
• The speed of the charged particle remains constant

This perpendicular force causes charged particles to move in circular or helical paths when entering a magnetic field.

Right-Hand Rules in Magnetism

Right-hand rules are essential tools for determining the direction of magnetic forces and fields:

• Right-hand rule for force: Point your fingers in the direction of velocity, curl them toward the magnetic field, and your thumb points in the direction of force on a positive charge.
• Right-hand thumb rule: Point the thumb in the direction of current; curled fingers show the direction of the magnetic field around a conductor.

For negative charges, the force direction is opposite to that given by the right-hand rule.

Motion of Charged Particles in a Magnetic Field

When a charged particle enters a magnetic field perpendicular to its velocity, it undergoes uniform circular motion. The radius of the circular path is given by:

r = mv / (qB)

where m is the mass of the particle.

If the velocity has a component parallel to the magnetic field, the particle follows a helical path. This principle is applied in devices such as cyclotrons and mass spectrometers.

Magnetic Force on a Current-Carrying Conductor

A current-carrying conductor placed in a magnetic field experiences a force described by:

F = BIL sinθ

where I is the current, L is the length of the conductor in the magnetic field, and θ is the angle between the conductor and the magnetic field.

This force is the working principle behind electric motors, where electrical energy is converted into mechanical energy.

Torque on a Current Loop

A rectangular current loop in a magnetic field experiences a torque that tends to rotate the loop. The torque is given by:

τ = NIAB sinθ

where N is the number of turns, A is the area of the loop, and θ is the angle between the normal to the loop and the magnetic field.

This concept is essential for understanding electric motors and galvanometers.

Magnetic Field Due to Current

Electric currents produce magnetic fields. Important cases include:

• Long straight conductor: B = μ₀I / (2πr)
• Circular loop: B = μ₀I / (2R) at the center
• Solenoid: B = μ₀nI inside the solenoid

Here, μ₀ is the permeability of free space, and n is the number of turns per unit length.

Electromagnetic Induction

Electromagnetic induction occurs when a changing magnetic flux induces an electromotive force (emf) in a conductor. This phenomenon is governed by Faraday’s Law:

ε = – dΦ / dt

The negative sign represents Lenz’s Law, which states that the induced emf opposes the change in magnetic flux that produced it.

Magnetic flux is defined as:

Φ = BA cosθ

Lenz’s Law and Conservation of Energy

Lenz’s Law ensures the conservation of energy in electromagnetic processes. If the induced current enhanced the change in magnetic flux instead of opposing it, energy would be created from nothing.

NMAT questions often test conceptual understanding of Lenz’s Law by asking for the direction of induced current when a magnet approaches or recedes from a loop.

Applications of Magnetism

Magnetism plays a crucial role in modern technology, including:

• Electric motors and generators
• Transformers
• Magnetic resonance imaging (MRI)
• Hard drives and data storage
• Speakers and microphones

Understanding the underlying physics helps NMAT examinees connect theoretical concepts to real-world applications.

Common NMAT Pitfalls in Magnetism

Students often make mistakes in magnetism-related questions due to:

• Incorrect application of right-hand rules
• Forgetting that magnetic force does no work
• Confusing electric and magnetic fields
• Ignoring angle dependence in formulas

Careful reading of the question and proper vector analysis can help avoid these errors.

NMAT Exam Tips for Magnetism

To excel in magnetism questions on the NMAT:

• Memorize key formulas and understand their derivations
• Practice direction-based problems using right-hand rules
• Visualize magnetic fields and forces
• Review common applications like motors and generators

Conceptual clarity combined with regular practice is the key to mastering magnetism for the NMAT.

Conclusion

Magnetism is a vital component of the NMAT Physics syllabus and an extension of fundamental concepts in electricity and motion. By understanding magnetic fields, forces on charges and currents, and electromagnetic induction, students can confidently tackle a wide range of exam questions. This review serves as a solid foundation, but consistent problem-solving and conceptual reinforcement are essential for achieving a high NMAT score.

Problem Sets

1. A proton (charge +1.6 × 10^-19 C) moves with a speed of 3.0 × 10⁶ m/s perpendicular to a uniform magnetic field of 0.50 T.
   What is the magnitude of the magnetic force acting on the proton?
2. An electron enters a uniform magnetic field of 0.20 T with a velocity of 4.0 × 10⁶ m/s at an angle of 30° to the field.
   What is the magnitude of the magnetic force on the electron? (Use |q| = 1.6 × 10^-19 C)
3. A charged particle with charge +2.0 × 10^-6 C moves at 500 m/s through a magnetic field of 0.80 T.
   If the force measured is 6.4 × 10^-4 N, what is the angle between the velocity and the magnetic field?
4. A wire of length 0.40 m carries a current of 8.0 A in a magnetic field of 0.60 T.
   If the wire is perpendicular to the magnetic field, what is the force on the wire?
5. A straight wire carrying 12 A is placed in a 0.50 T magnetic field. The wire length in the field is 0.25 m and makes an angle of 60° with the field.
   Find the magnitude of the force on the wire.
6. A proton moves in a circle of radius 0.12 m in a uniform magnetic field of 0.80 T (perpendicular entry).
   If the proton mass is 1.67 × 10^-27 kg and charge is 1.6 × 10^-19 C, what is the proton’s speed?
7. An electron moves perpendicular to a magnetic field of 0.10 T and follows a circular path of radius 2.0 cm.
   If the electron mass is 9.11 × 10^-31 kg and charge magnitude is 1.6 × 10^-19 C, find the electron’s speed.
8. A long straight wire carries a current of 5.0 A.
   What is the magnitude of the magnetic field at a point 4.0 cm from the wire? (Use μ₀ = 4π × 10^-7 T·m/A)
9. A circular loop of radius 0.10 m carries a current of 3.0 A.
   What is the magnetic field at the center of the loop? (Use μ₀ = 4π × 10^-7 T·m/A)
10. A solenoid has 1200 turns and a length of 0.60 m, carrying a current of 2.5 A.
    Find the magnetic field inside the solenoid. (Use μ₀ = 4π × 10^-7 T·m/A)
11. A coil has 50 turns and area 0.020 m². The magnetic field through the coil changes uniformly from 0.10 T to 0.60 T in 0.20 s, with the field perpendicular to the coil.
    What is the magnitude of the induced emf?
12. A circular loop of area 0.015 m² is in a uniform magnetic field of 0.40 T. The loop is rotated so that the angle between the field and the loop’s normal changes from 0° to 60° in 0.50 s.
    What is the average induced emf? (Assume 1 turn.)
13. A conducting rod of length 0.50 m moves at 6.0 m/s perpendicular to a magnetic field of 0.30 T.
    What is the motional emf induced across the rod?
14. A rectangular loop is pulled out of a uniform magnetic field. As it leaves the field region, the magnetic flux through it decreases.
    According to Lenz’s law, does the induced current create a magnetic field in the same direction as the original field or the opposite direction?
15. A particle with charge +3.2 × 10^-19 C enters a magnetic field of 0.40 T with velocity 2.0 × 10⁶ m/s perpendicular to the field.
    What is the period of its circular motion if its mass is 6.6 × 10^-27 kg?

Answer Keys

1. F = qvB sinθ, θ = 90° → sinθ = 1
   F = (1.6 × 10^-19)(3.0 × 10⁶)(0.50)
   F = 2.4 × 10^-13 N
2. F = |q|vB sin30° = (1.6 × 10^-19)(4.0 × 10⁶)(0.20)(0.5)
   F = 6.4 × 10^-14 N
3. F = qvB sinθ → sinθ = F/(qvB)
   sinθ = (6.4 × 10^-4)/[(2.0 × 10^-6)(500)(0.80)]
   Denominator = 2.0 × 10^-6 × 500 = 1.0 × 10^-3; then × 0.80 = 8.0 × 10^-4
   sinθ = (6.4 × 10^-4)/(8.0 × 10^-4) = 0.80
   θ ≈ 53°
4. F = BIL sin90° = (0.60)(8.0)(0.40) = 1.92 N
5. F = BIL sin60° = (0.50)(12)(0.25)(0.866)
   (0.50)(12) = 6; 6(0.25) = 1.5; 1.5(0.866) ≈ 1.30 N
6. r = mv/(qB) → v = r(qB)/m
   v = (0.12)(1.6 × 10^-19)(0.80)/(1.67 × 10^-27)
   Numerator = 0.12 × 1.28 × 10^-19 = 1.536 × 10^-20
   v ≈ (1.536 × 10^-20)/(1.67 × 10^-27) ≈ 9.2 × 10⁶ m/s
7. v = r(qB)/m
   v = (0.020)(1.6 × 10^-19)(0.10)/(9.11 × 10^-31)
   Numerator = 3.2 × 10^-22
   v ≈ (3.2 × 10^-22)/(9.11 × 10^-31) ≈ 3.5 × 10⁸ m/s
8. B = μ₀I/(2πr)
   B = (4π × 10^-7)(5.0)/(2π × 0.040)
   Cancel π: B = (4 × 10^-7 × 5.0)/(2 × 0.040)
   Numerator = 2.0 × 10^-6; Denominator = 0.080
   B = 2.5 × 10^-5 T
9. B = μ₀I/(2R)
   B = (4π × 10^-7)(3.0)/(2 × 0.10)
   B = (12π × 10^-7)/0.20 = 60π × 10^-7
   B ≈ 1.9 × 10^-5 T
10. B = μ₀nI, where n = N/L = 1200/0.60 = 2000 m^-1
    B = (4π × 10^-7)(2000)(2.5)
    2000 × 2.5 = 5000
    B = 4π × 10^-7 × 5000 = 2π × 10^-3
    B ≈ 6.3 × 10^-3 T
11. ε = N A (ΔB/Δt) (since perpendicular, cosθ = 1)
    ε = 50(0.020)[(0.60 – 0.10)/0.20]
    ΔB/Δt = 0.50/0.20 = 2.5 T/s
    ε = 50(0.020)(2.5) = 1.0(2.5) = 2.5 V
12. Average emf: ε_avg = |ΔΦ|/Δt, Φ = BA cosθ
    Initial: θ = 0° → Φ_i = BA(1) = (0.40)(0.015) = 0.006 Wb
    Final: θ = 60° → Φ_f = BA cos60° = 0.006(0.5) = 0.003 Wb
    |ΔΦ| = 0.003 Wb
    ε_avg = 0.003/0.50 = 0.006 V
13. Motional emf: ε = BLv
    ε = (0.30)(0.50)(6.0) = 0.90 V
14. The loop opposes the decrease in flux, so it produces a magnetic field in the same direction as the original field.
15. Period in magnetic field: T = 2πm/(qB)
    T = 2π(6.6 × 10^-27)/[(3.2 × 10^-19)(0.40)]
    Denominator = 1.28 × 10^-19
    T ≈ 2π(5.16 × 10^-8) ≈ 3.24 × 10^-7 s

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