Class 12 Physics NCERT Solutions: Moving Charges and Magnetism Important Questions

Class 12 Physics is a crucial part of the senior secondary curriculum, and it lays the foundation for students planning to pursue careers in engineering, research, or other science-related fields. One of the vital chapters in the NCERT Physics textbook for Class 12 is "Moving Charges and Magnetism." This chapter introduces students to the fundamentals of electromagnetism, covering various aspects such as magnetic force, magnetic field, and motion of charged particles in a magnetic field. In this article, we will provide a comprehensive guide to "Moving Charges and Magnetism," along with important questions, solutions, and concepts to help students excel in their exams.

Chapter Overview: Moving Charges and Magnetism

The chapter "Moving Charges and Magnetism" is based on the study of magnetic fields created by moving electric charges. This is a core concept in electromagnetism that has numerous applications in technology and physics. Some of the critical topics covered in this chapter are:

1. Magnetic Force: Force experienced by a moving charge in a magnetic field.
2. Magnetic Field: The area around a magnet or current-carrying conductor where magnetic forces can be detected.
3. Biot-Savart Law: An equation describing the magnetic field generated by a steady current.
4. Ampere's Circuital Law: A law that relates the integrated magnetic field around a closed loop to the electric current passing through the loop.
5. Motion of Charged Particles in a Magnetic Field: Analysis of the circular and helical paths of charged particles when they move perpendicular or at an angle to the magnetic field.
6. Cyclotron: A device used to accelerate charged particles to high speeds using magnetic and electric fields.
7. Force Between Two Parallel Currents: The magnetic interaction between two current-carrying conductors.

Important Concepts and Formulas

1. Magnetic Force on a Moving Charge:

   • Formula: F = q(v × B)
   • Here, F is the magnetic force, q is the electric charge, v is the velocity of the charge, and B is the magnetic field.
   • The direction of the magnetic force is given by the right-hand rule.

2. Magnetic Field due to a Current-Carrying Conductor (Biot-Savart Law):

   • Formula: dB = (μ₀/4π) * (Idl × r̂) / r²
   • Where dB is the infinitesimal magnetic field, μ₀ is the permeability of free space, I is the current, dl is the length element of the conductor, and r̂ is the unit vector.

3. Ampere's Circuital Law:

   • Formula: ∮B · dl = μ₀I
   • This law states that the line integral of the magnetic field B around a closed loop is equal to μ₀ times the total current I passing through the loop.

4. Motion of Charged Particles in a Magnetic Field:

   • Radius of the circular path: r = (mv)/(qB)
   • Time period of revolution: T = (2πm)/(qB)
   • Here, m is the mass of the charged particle, v is the velocity, q is the charge, and B is the magnetic field.

5. Cyclotron Frequency:

   • Formula: f = (qB)/(2πm)
   • The cyclotron is used to accelerate charged particles, and its frequency depends on the charge and mass of the particle and the magnetic field.

6. Force Between Two Parallel Conductors:

   • Formula: F/L = (μ₀I₁I₂)/(2πd)
   • Where F is the force, L is the length of the conductors, I₁ and I₂ are the currents, d is the distance between the conductors, and μ₀ is the permeability of free space.

Important Questions and Solutions

To score well in Class 12 Physics exams, students must practice various types of questions that cover all the essential topics from the chapter. Below are some important questions along with their solutions:

Question 1: Derive the expression for the magnetic force experienced by a charged particle moving in a uniform magnetic field.

Solution: The magnetic force F experienced by a charged particle of charge q moving with velocity v in a magnetic field B is given by:

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

Here, the cross product ($\mathbf{v} \times \mathbf{B}$) implies that the force is perpendicular to both the velocity of the particle and the magnetic field. The magnitude of the force can be expressed as:

$F = qvB \sin \theta$

where $\theta$ is the angle between the velocity vector and the magnetic field. This equation shows that the magnetic force is maximum when the angle is 90° (i.e., when the velocity is perpendicular to the magnetic field) and zero when the velocity is parallel or antiparallel to the magnetic field.

Question 2: State and derive Biot-Savart Law for the magnetic field due to a small element of current-carrying wire.

Solution: The Biot-Savart Law gives the magnetic field dB at a point due to a small element of a current-carrying conductor. According to the Biot-Savart Law:

$dB = \frac{{\mu_0}}{4\pi} \frac{{I \, d\mathbf{l} \times \mathbf{r}}}{r^3}$

where:

• $I$ is the current through the conductor,
• $d\mathbf{l}$ is a small element of the conductor,
• $\mathbf{r}$ is the vector from the element to the point where the magnetic field is being calculated,
• $\mu_0$ is the permeability of free space.

The direction of dB is perpendicular to the plane formed by $d\mathbf{l}$ and $\mathbf{r}$, and the magnitude is given by:

$dB = \frac{{\mu_0 I \, d\mathbf{l} \sin \theta}}{4\pi r^2}$

where $\theta$ is the angle between $d\mathbf{l}$ and $\mathbf{r}$.

Question 3: Explain Ampere’s Circuital Law and apply it to find the magnetic field inside a long straight solenoid.

Solution: Ampere’s Circuital Law states that the line integral of the magnetic field around a closed loop is equal to $\mu_0$ times the total current enclosed by the loop:

$\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_{\text{enc}}$

For a long solenoid with n turns per unit length and current I flowing through it, the magnetic field inside the solenoid is uniform and parallel to its length. Applying Ampere’s Circuital Law to a rectangular loop around the solenoid:

$B \cdot l = \mu_0 n I \, l$

where l is the length of the loop inside the solenoid. Solving for B, we get:

$B = \mu_0 n I$

This shows that the magnetic field inside a long solenoid is directly proportional to the current and the number of turns per unit length.

Question 4: A proton is moving perpendicular to a uniform magnetic field of 0.5 T with a speed of $2 \times 10^6$ m/s. Calculate the radius of its circular path.

Solution: The radius $r$ of the circular path of a charged particle moving perpendicular to a magnetic field is given by:

$r = \frac{mv}{qB}$

For a proton:

• Mass, $m = 1.67 \times 10^{-27}$ kg
• Charge, $q = 1.6 \times 10^{-19}$ C
• Velocity, $v = 2 \times 10^6$ m/s
• Magnetic field, $B = 0.5$ T

Substitute the values:

$r = \frac{(1.67 \times 10^{-27}) \times (2 \times 10^6)}{(1.6 \times 10^{-19}) \times 0.5}$

$r \approx 0.0418 \, \text{m}$

Therefore, the radius of the proton's circular path is approximately 0.042 meters.

Question 5: What is a cyclotron? Derive the expression for the maximum kinetic energy of a particle accelerated by a cyclotron.

Solution: A cyclotron is a device used to accelerate charged particles to high speeds using a combination of electric and magnetic fields. It consists of two hollow D-shaped electrodes called dees, placed in a perpendicular magnetic field. An alternating voltage applied between the dees accelerates the particles.

The cyclotron frequency $f$ is given by:

$f = \frac{qB}{2\pi m}$

The maximum kinetic energy $K_{\text{max}}$ of a particle accelerated by a cyclotron is:

$K_{\text{max}} = \frac{1}{2} mv^2 = \frac{q^2 B^2 R^2}{2m}$

where R is the maximum radius of the particle's path.

Tips for Answering Questions Effectively

1. Understand the Concepts: Thoroughly study the NCERT textbook and understand each concept.
2. Use Diagrams: Diagrams play a crucial role in explaining concepts in Physics. Draw neat and labeled diagrams wherever necessary.
3. Apply Formulas Correctly: Practice solving problems to understand the application of formulas in different contexts.
4. Revise Regularly: Regular revision is essential to retain concepts and formulas.
5. Practice Previous Year Questions: Solve previous years' questions to get an idea of the type of questions asked in exams.

Conclusion

The chapter "Moving Charges and Magnetism" is an essential part of the Class 12 Physics syllabus, with applications ranging from daily life to advanced technology. Understanding the concepts, practicing numerical problems, and being thorough with the NCERT solutions can help students perform well in their board exams. The important questions and solutions provided in this article will be beneficial for students in their preparation journey, helping them to excel in the topic of electromagnetism.