Physics plays a vital role in understanding the basic principles governing the natural world. One such significant topic in Class 12 Physics is Moving Charges and Magnetism. This chapter connects two essential concepts: electricity and magnetism.

We have learned that a stationary charge produces an electric field. However, when the charge moves, it produces both electric and magnetic fields. The relationship between electricity and magnetism was first discovered by Hans Christian Ørsted in 1820 when he found that an electric current can deflect a magnetic needle. This observation laid the foundation of Electromagnetism.

In this chapter, we will cover concepts such as magnetic force, motion of charged particles in magnetic fields, Biot–Savart law, Ampere’s law, solenoids, torque on current loops, and much more in detail.

Moving Charges and Magnetism Class 12 Physics Notes | Detailed Explanation & Questions

Concept of Magnetic Field

A magnetic field is a region around a magnet or a current-carrying conductor in which the force of magnetism acts.

• Denoted by B

• Measured in Tesla (T)

• A moving charge or current element produces a magnetic field.

Right-Hand Thumb Rule

• Imagine holding the current-carrying conductor in your right hand with the thumb pointing in the direction of the current.

• The curl of your fingers gives the direction of the magnetic field lines.

Magnetic Force on a Moving Charge

When a charge q moves with velocity v in a magnetic field B, it experiences a force given by

$$F=q(\mathbf{v}\times \mathbf{B})$$

• Direction of F is given by the Right-Hand Rule.

• The force is always perpendicular to both velocity and magnetic field.

• If v is parallel or antiparallel to B, no force acts on the particle.

Magnetic Force on Current-Carrying Conductor

A conductor carrying current I in a magnetic field experiences a force:

$$F=ILB\sin \theta$$

where L is the length of the conductor in the field.

Motion of a Charged Particle in a Magnetic Field

• When a charged particle enters a magnetic field perpendicular to its velocity, it experiences a centripetal force leading to circular motion.

• Radius of the circle:

r=mvqBr = \frac{mv}{qB}r=qBmv​

• Time period of revolution:

T=2πmqBT = \frac{2\pi m}{qB}T=qB2πm​

• Frequency:

f=1T=qB2πmf = \frac{1}{T} = \frac{qB}{2\pi m}f=T1​=2πmqB​

This principle is used in Cyclotrons for accelerating particles.

Biot–Savart Law

It gives the magnetic field produced at a point due to a small current element.

Mathematical form:

dB=μ04πIdlsin⁡θr2dB = \frac{\mu_0}{4\pi} \frac{Idl \sin\theta}{r^2}dB=4πμ0​​r2Idlsinθ​

Where:

• I = current

• dl = length element

• θ = angle between dl and position vector

• r = distance from element to point

Magnetic Field due to Current in a Straight Conductor

The magnetic field at a point at a distance r from a long straight current-carrying conductor:

B=μ0I2πrB = \frac{\mu_0 I}{2 \pi r}B=2πrμ0​I​

Magnetic Field on the Axis of a Circular Current Loop

For a circular loop of radius R, the magnetic field at a distance x on its axis is:

B=μ0IR22(R2+x2)3/2B = \frac{\mu_0 I R^2}{2 (R^2 + x^2)^{3/2}}B=2(R2+x2)3/2μ0​IR2​

Ampere’s Circuital Law

It states that:

∮B⋅dl=μ0Ienc\oint B \cdot dl = \mu_0 I_{enc}∮B⋅dl=μ0​Ienc​

This law helps in calculating magnetic fields in symmetric situations like solenoids and toroids.

Magnetic Field inside a Solenoid

A solenoid is a coil of many turns of wire, closely wound.

• Magnetic field inside a long solenoid:

B=μ0nIB = \mu_0 n IB=μ0​nI

Where n = number of turns per unit length

A solenoid produces a uniform magnetic field similar to a bar magnet.

Magnetic Field in a Toroid

A toroid is a solenoid bent into a circular shape.

• Magnetic field inside a toroid:

B=μ0NI2πrB = \frac{\mu_0 N I}{2 \pi r}B=2πrμ0​NI​

Where N = total number of turns, r = radius of toroid.

Force between Two Parallel Current-Carrying Conductors

Two parallel conductors carrying currents I₁ and I₂ separated by a distance d exert forces on each other:

FL=μ0I1I22πd\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2 \pi d}LF​=2πdμ0​I1​I2​​

• Same direction currents → Attraction

• Opposite direction currents → Repulsion

Torque on a Current Loop

A current loop placed in a magnetic field experiences torque:

$$\tau =NIAB\sin \theta$$

Where N = number of turns, A = area of loop.

Magnetic Dipole Moment

• A current loop behaves like a magnetic dipole.

• Magnetic dipole moment:

$$M=IA$$

Galvanometer

• A device used to detect current.

• Works on the principle of torque on current loop in a magnetic field.

• Can be converted into Ammeter or Voltmeter using shunt or series resistance.

Cyclotron

• A device to accelerate charged particles using electric and magnetic fields.

• Used in nuclear physics and medical applications.

Summary Table

Q1. Magnetic field is measured in:

a) Tesla
b) Weber
c) Volt
d) Ohm
Answer: a) Tesla

Q2. A moving charge produces:

a) Only electric field
b) Only magnetic field
c) Both electric & magnetic fields
d) No field
Answer: c) Both electric & magnetic fields

Q3. Magnetic force on a charge is zero when velocity is:

a) Perpendicular to field
b) Parallel to field
c) At 90° to field
d) None
Answer: b) Parallel to field

Q4. The SI unit of magnetic dipole moment:

a) T m²
b) A m²
c) N m
d) A/T
Answer: b) A m²

Q5. Biot–Savart law is analogous to:

a) Coulomb’s Law
b) Ohm’s Law
c) Ampere’s Law
d) Gauss’s Law
Answer: a) Coulomb’s Law

Q6. Magnetic field at center of circular loop of radius R is proportional to:

a) 1/R
b) R²
c) 1/R²
d) R
Answer: a) 1/R

Q7. Ampere’s law is used to calculate field of:

a) Bar magnet
b) Solenoid
c) Earth
d) All
Answer: b) Solenoid

Q8. Magnetic field in a toroid is:

a) Uniform inside
b) Zero outside
c) Both a & b
d) None
Answer: c) Both a & b

Q9. Cyclotron accelerates:

a) Neutrons
b) Protons & ions
c) Photons
d) None
Answer: b) Protons & ions

Q10. Force per unit length between two wires is proportional to:

a) Product of currents
b) Sum of currents
c) Square of currents
d) Difference of currents
Answer: a) Product of currents

Q11. Right-hand thumb rule gives:

a) Field direction
b) Current direction
c) Force direction
d) None
Answer: a) Field direction

Q12. SI unit of magnetic field:

a) Tesla
b) Gauss
c) Weber
d) Henry
Answer: a) Tesla

Q13. Magnetic field inside long solenoid is:

a) Non-uniform
b) Zero
c) Uniform
d) Infinite
Answer: c) Uniform

Q14. Torque on current loop is maximum when:

a) θ = 0°
b) θ = 90°
c) θ = 180°
d) θ = 360°
Answer: b) θ = 90°

Q15. Magnetic field of Earth is due to:

a) Sunlight
b) Electric currents in Earth’s core
c) Wind currents
d) None
Answer: b) Electric currents in Earth’s core

Q16. The direction of magnetic field lines is from:

a) South to North
b) North to South
c) North to South inside & South to North outside
d) North to South outside & South to North inside
Answer: d) North to South outside & South to North inside

Q17. Lorentz force involves:

a) Electric field only
b) Magnetic field only
c) Both electric & magnetic fields
d) None
Answer: c) Both electric & magnetic fields

Q18. Force on moving charge depends on:

a) Speed
b) Field strength
c) Angle between v & B
d) All
Answer: d) All

Q19. Magnetic field outside a long solenoid:

a) Strong
b) Zero
c) Non-uniform
d) Infinite
Answer: b) Zero

Q20. Magnetic moment of current loop:

a) Proportional to current
b) Inversely to area
c) Proportional to area
d) Both a & c
Answer: d) Both a & c

Short Answer Questions

Q1. What is the right-hand thumb rule?

Answer: It states that if the right hand grips a conductor with the thumb pointing in the direction of current, then the curl of the fingers shows the direction of the magnetic field.

Q2. Define Lorentz Force.

Answer: The total force on a charge moving in both electric & magnetic fields is called the Lorentz force:

$$F=q(E+v\times B)$$

Q3. Why is the magnetic field inside a long solenoid uniform?

Answer: Due to closely spaced turns and superposition of fields, the field lines inside are parallel and equally spaced, making the field uniform.

Long Answer Questions

Q1. Derive expression for magnetic field inside a long solenoid.

Answer:
Using Ampere’s Law for a rectangular Amperian loop inside a solenoid,

∮B⋅dl=μ0nI×l\oint B \cdot dl = \mu_0 n I \times l∮B⋅dl=μ0​nI×l

Hence,

B=μ0nIB = \mu_0 n IB=μ0​nI

Q2. Explain the working of a Cyclotron.

Answer:
A cyclotron uses a magnetic field to bend particle paths into circular orbits and an alternating electric field to accelerate them across the gap between two D-shaped electrodes. Each time particles cross the gap, they gain energy until they reach the desired velocity.

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FAQs

Q1. What is the unit of magnetic field?

Answer: Tesla (T).

Q2. Which law helps calculate the field of a solenoid?

Answer: Ampere’s Circuital Law.

Q3. What is the principle of Galvanometer?

Answer: Torque on a current-carrying loop in a magnetic field.

Q4. When is magnetic force on a moving charge zero?

Answer: When velocity is parallel to the magnetic field.

Q5. What is the significance of moving charges?

Answer: They produce magnetic fields, forming the basis of electromagnetism

Conclusion

The chapter Moving Charges and Magnetism bridges electricity and magnetism, explaining how moving charges produce magnetic fields and how these fields influence charges and currents. It forms the basis of modern devices like motors, galvanometers, and cyclotrons. A clear understanding of formulas, laws, and applications helps in scoring well in exams as well as in building strong conceptual knowledge.

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