CBSE Class 12 Physics (2026–27)
Chapter 4: Moving Charges and Magnetism
20 Important Questions and Answers
Q1. What is the Lorentz force? Write its expression.
Answer:
Lorentz force is the total force experienced by a charged particle moving in electric and magnetic fields simultaneously. It is one of the fundamental concepts in electromagnetism. If a particle having charge (q) moves with velocity (v) in an electric field (E) and magnetic field (B), the Lorentz force is given by:
[F = q(E + v \times B)]
The electric component (qE) acts along the electric field, while the magnetic component (q(v \times B)) acts perpendicular to both velocity and magnetic field. The magnetic force changes only the direction of motion and not the speed of the particle. This principle is used in devices such as cyclotrons, mass spectrometers, and particle accelerators.
Q2. State the force acting on a moving charge in a magnetic field.
Answer:
A charged particle moving in a magnetic field experiences a magnetic force. The magnitude of this force is given by:
[F = qvB\sin\theta]
where (q) is the charge, (v) is the velocity of the particle, (B) is the magnetic field strength, and (\theta) is the angle between velocity and magnetic field. The force is maximum when the particle moves perpendicular to the magnetic field and zero when it moves parallel to the field. The direction of force is determined by Fleming’s Left-Hand Rule for positive charges and is opposite for negative charges. This force causes the particle to move in a circular path without changing its speed.
Q3. Explain the motion of a charged particle in a uniform magnetic field.
Answer:
When a charged particle enters a uniform magnetic field perpendicular to the field lines, it experiences a magnetic force that always acts at right angles to its velocity. This force acts as a centripetal force and makes the particle move in a circular path. The radius of the path is given by:
[r=\frac{mv}{qB}]
where (m) is the mass of the particle. Since the magnetic force is always perpendicular to motion, it does no work on the particle. Therefore, the speed and kinetic energy remain constant. If the particle enters the field at an angle, it follows a helical path. Such motion is important in cyclotrons and particle accelerators.
Q4. What is the radius of the circular path of a charged particle in a magnetic field?
Answer:
When a charged particle moves perpendicular to a uniform magnetic field, it follows a circular path because the magnetic force acts as the centripetal force. Equating magnetic force and centripetal force:
[qvB=\frac{mv^2}{r}]
Hence, the radius of the circular path is:
[r=\frac{mv}{qB}]
The radius depends directly on the particle’s mass and velocity and inversely on the magnetic field strength and charge. Thus, heavier particles or particles moving faster have larger radii, while stronger magnetic fields produce smaller radii. This relation helps in identifying charged particles and is widely used in mass spectrometers and particle detectors.
Q5. Define cyclotron frequency and derive its expression.
Answer:
Cyclotron frequency is the frequency with which a charged particle revolves in a magnetic field. For circular motion:
[qvB=\frac{mv^2}{r}]
Therefore,
[\frac{v}{r}=\frac{qB}{m}]
Since angular velocity (\omega = \frac{v}{r}),
[\omega=\frac{qB}{m}]
The cyclotron frequency is:
[f=\frac{\omega}{2\pi}]
[f=\frac{qB}{2\pi m}]
This frequency depends only on the charge-to-mass ratio and magnetic field strength. It is independent of the particle’s speed and radius. Cyclotron frequency is an important concept used in cyclotrons to accelerate charged particles to high energies.
Q6. State and explain Biot–Savart Law.
Answer:
Biot–Savart Law gives the magnetic field produced at a point due to a small current-carrying element. According to the law, the magnetic field is directly proportional to the current, length of the conductor element, and sine of the angle between them, and inversely proportional to the square of the distance.
Mathematically,
[dB=\frac{\mu_0}{4\pi}\frac{Idl\sin\theta}{r^2}]
The direction of the magnetic field is determined by the right-hand thumb rule. Biot–Savart Law is analogous to Coulomb’s law in electrostatics and is used to calculate magnetic fields due to current-carrying wires, circular loops, and solenoids.
Q7. State Ampere’s Circuital Law.
Answer:
Ampere’s Circuital Law relates the magnetic field around a closed path to the current enclosed by that path. It states that the line integral of the magnetic field around any closed loop is equal to (\mu_0) times the total current enclosed.
Mathematically,
[\oint B \cdot dl = \mu_0 I]
where (B) is the magnetic field, (dl) is a small element of the path, and (I) is the enclosed current. This law is useful for calculating magnetic fields of symmetrical current distributions such as long straight conductors, solenoids, and toroids. It simplifies calculations where Biot–Savart Law becomes complex.
Q8. Obtain the expression for magnetic field due to a long straight conductor.
Answer:
Using Ampere’s Circuital Law, consider a circular path of radius (r) around a long straight conductor carrying current (I).
[\oint B\cdot dl = \mu_0 I]
Since the magnetic field is constant on the circular path,
[B(2\pi r)=\mu_0 I]
Therefore,
[B=\frac{\mu_0 I}{2\pi r}]
The magnetic field is directly proportional to the current and inversely proportional to the distance from the conductor. The direction of the field is given by the right-hand thumb rule. This relation is widely used in electrical engineering and electromagnetic applications.
Q9. What is Fleming’s Left-Hand Rule?
Answer:
Fleming’s Left-Hand Rule is used to determine the direction of force acting on a current-carrying conductor placed in a magnetic field. According to this rule, stretch the thumb, forefinger, and middle finger of the left hand mutually perpendicular to each other. If the forefinger represents the magnetic field direction and the middle finger represents the current direction, then the thumb indicates the direction of force or motion.
This rule is based on the interaction between magnetic fields and electric currents. It is widely used in electric motors to predict the direction of rotation and understand electromagnetic force on conductors.
Q10. Define magnetic dipole moment of a current loop.
Answer:
The magnetic dipole moment of a current-carrying loop is a vector quantity that represents the strength and orientation of the magnetic dipole. It is defined as the product of current flowing through the loop and the area enclosed by the loop.
[M = IA]
where (I) is the current and (A) is the area of the loop. Its direction is perpendicular to the plane of the loop and is determined by the right-hand thumb rule. The SI unit of magnetic dipole moment is A·m². It determines how strongly a loop interacts with an external magnetic field.
Q11. What is the torque acting on a current loop in a magnetic field?
Answer:
A current-carrying loop placed in a magnetic field experiences a torque that tends to rotate it. The torque is given by:
[\tau = MB\sin\theta]
where (M) is the magnetic dipole moment, (B) is the magnetic field strength, and (\theta) is the angle between them. The torque is maximum when the plane of the loop is parallel to the magnetic field and zero when the magnetic moment is aligned with the field. This principle is used in moving-coil galvanometers, electric motors, and various electromagnetic instruments.
Q12. Define moving coil galvanometer.
Answer:
A moving coil galvanometer is a sensitive instrument used to detect and measure small electric currents. It consists of a rectangular coil suspended between the poles of a strong permanent magnet. When current flows through the coil, a magnetic torque acts on it, causing it to rotate.
The deflection produced is proportional to the current passing through the coil. A spring provides restoring torque to balance the magnetic torque. The galvanometer works on the principle that a current-carrying conductor experiences torque in a magnetic field. It can be converted into an ammeter or voltmeter by suitable modifications.
Q13. What is the sensitivity of a galvanometer?
Answer:
Sensitivity of a galvanometer indicates its ability to detect small currents. It is defined as the deflection produced per unit current flowing through the coil.
[S=\frac{\theta}{I}]
where (\theta) is the angular deflection and (I) is the current. A galvanometer with higher sensitivity gives larger deflection for a small current. Sensitivity can be increased by increasing the number of turns, magnetic field strength, and coil area while decreasing the restoring torque. Highly sensitive galvanometers are used in laboratories for accurate current measurements and experimental investigations.
Q14. How can a galvanometer be converted into an ammeter?
Answer:
A galvanometer is converted into an ammeter by connecting a low-resistance shunt in parallel with it. The shunt allows most of the current to bypass the galvanometer coil, protecting it from damage due to large currents.
If (G) is the galvanometer resistance and (S) is the shunt resistance, then:
[S=\frac{I_gG}{I-I_g}]
where (I_g) is the galvanometer current and (I) is the desired current range. The resulting instrument has very low resistance and is connected in series in a circuit. Thus, it can measure large currents accurately.
Q15. How can a galvanometer be converted into a voltmeter?
Answer:
A galvanometer can be converted into a voltmeter by connecting a high resistance in series with it. This high resistance limits the current passing through the galvanometer when a potential difference is applied.
If (R) is the required resistance, then:
[R=\frac{V}{I_g}-G]
where (V) is the voltage range, (I_g) is galvanometer current, and (G) is galvanometer resistance. The voltmeter thus formed has very high resistance and is connected in parallel across the component whose voltage is to be measured. This ensures negligible current is drawn from the circuit.
Q16. Why does a magnetic field do no work on a moving charge?
Answer:
The magnetic force acting on a moving charge is always perpendicular to the velocity of the charge. Since work done is given by:
[W = Fd\cos\theta]
and the angle between magnetic force and displacement is (90^\circ),
[W = 0]
Therefore, a magnetic field does no work on a moving charge. Although the direction of motion changes, the speed and kinetic energy remain constant. The magnetic field only changes the direction of velocity, producing circular or helical motion. This property is important in particle accelerators and magnetic confinement systems.
Q17. State the right-hand thumb rule.
Answer:
The right-hand thumb rule is used to determine the direction of the magnetic field around a straight current-carrying conductor. According to this rule, if the conductor is held in the right hand such that the thumb points in the direction of current, then the curled fingers indicate the direction of magnetic field lines around the conductor.
This rule helps visualize the circular magnetic field produced by electric current. It is widely used in electromagnetism and forms the basis for understanding magnetic effects of current in wires, loops, and coils.
Q18. What is a solenoid? Mention its magnetic properties.
Answer:
A solenoid is a long cylindrical coil consisting of many closely wound turns of insulated wire. When electric current passes through it, a strong magnetic field is produced inside the coil.
The magnetic field inside a long solenoid is nearly uniform and parallel to its axis. The field strength is given by:
[B=\mu_0 nI]
where (n) is the number of turns per unit length and (I) is the current. A solenoid behaves like a bar magnet with distinct north and south poles. It is widely used in electromagnets, relays, electric bells, and magnetic switches.
Q19. What is the force between two parallel current-carrying conductors?
Answer:
Two parallel current-carrying conductors exert magnetic forces on each other. If the currents flow in the same direction, the conductors attract each other; if they flow in opposite directions, they repel each other.
The force per unit length between them is:
[\frac{F}{L}=\frac{\mu_0 I_1 I_2}{2\pi d}]
where (I_1) and (I_2) are the currents and (d) is the distance between the conductors. This phenomenon forms the basis for the definition of the ampere and demonstrates the magnetic interaction between electric currents.
Q20. Distinguish between magnetic field lines and electric field lines.
Answer:
Magnetic field lines and electric field lines represent the direction and strength of magnetic and electric fields respectively. Electric field lines originate from positive charges and terminate at negative charges. In contrast, magnetic field lines always form closed loops and do not have starting or ending points because magnetic monopoles do not exist.
Electric field lines can exist independently around charges, whereas magnetic field lines are produced by moving charges or magnets. The density of both types of lines indicates field strength. Understanding these field patterns helps explain electromagnetic interactions and field distributions around charges and magnets.