1. What is the origin of magnetism in materials? Explain with reference to the atomic theory and electron spin.
Answer: The origin of magnetism in materials lies in the alignment of electron spins within atoms. According to the atomic theory, electrons possess a property called spin, which can be either up or down. When these electron spins align in a particular direction, they create a magnetic field. In materials, such as iron, nickel, and cobalt, the electron spins align due to interactions between neighboring atoms, resulting in a net magnetic field.
2. How does the magnetic field produced by a current-carrying wire depend on the distance from the wire? Explain using Ampere’s law and the concept of magnetic field lines.
Answer: According to Ampere’s law, the magnetic field produced by a current-carrying wire is directly proportional to the current flowing through the wire and inversely proportional to the distance from the wire. This relationship can be understood by considering the concept of magnetic field lines. Magnetic field lines form closed loops around the wire, and the density of these lines decreases as the distance from the wire increases. Therefore, the magnetic field strength decreases with increasing distance from the wire.
3. How does the strength of the magnetic field inside a solenoid depend on the number of turns and the current flowing through it? Explain using the Biot-Savart law and the concept of magnetic flux.
Answer: The strength of the magnetic field inside a solenoid is directly proportional to the number of turns of the coil and the current flowing through it. This relationship can be derived from the Biot-Savart law, which states that the magnetic field produced by a current element is directly proportional to the current, the length of the element, and the sine of the angle between the element and the direction of the magnetic field. In a solenoid, the magnetic field lines are tightly packed due to the large number of turns, resulting in a stronger magnetic field.
4. How does the force experienced by a current-carrying conductor placed in a magnetic field depend on the length of the conductor and the strength of the magnetic field? Explain using the Lorentz force law and the concept of magnetic flux density.
Answer: The force experienced by a current-carrying conductor placed in a magnetic field is directly proportional to the length of the conductor, the strength of the magnetic field, and the current flowing through the conductor. This relationship can be derived from the Lorentz force law, which states that the force on a charged particle moving through a magnetic field is given by the product of the charge, the velocity of the particle, and the magnetic flux density. In the case of a current-carrying conductor, the Lorentz force acts perpendicular to both the current direction and the magnetic field direction.
5. How does the torque experienced by a current loop placed in a magnetic field depend on the area of the loop and the strength of the magnetic field? Explain using the principle of magnetic moments and the concept of magnetic torque.
Answer: The torque experienced by a current loop placed in a magnetic field is directly proportional to the area of the loop, the strength of the magnetic field, and the current flowing through the loop. This relationship can be understood by considering the principle of magnetic moments. A current loop generates a magnetic moment, which is the product of the current, the area of the loop, and the vector normal to the loop’s plane. When this magnetic moment interacts with an external magnetic field, a torque is exerted on the loop, causing it to rotate. The magnitude of this torque is directly proportional to the product of the magnetic moment and the magnetic field strength.
6. How does the induced emf in a coil depend on the rate of change of magnetic flux through the coil? Explain using Faraday’s law of electromagnetic induction and Lenz’s law.
Answer: The induced emf in a coil is directly proportional to the rate of change of magnetic flux through the coil. This relationship can be explained by Faraday’s law of electromagnetic induction, which states that the magnitude of the induced emf is equal to the rate of change of magnetic flux. Lenz’s law further states that the induced current flows in such a direction as to oppose the change in magnetic flux that produced it. Therefore, when the magnetic flux through a coil changes, an emf is induced in the coil, which in turn generates a current that opposes the change in flux.
7. How does the self-inductance of a coil depend on the number of turns and the permeability of the core material? Explain using the concept of magnetic field energy and the formula for self-inductance.
Answer: The self-inductance of a coil is directly proportional to the number of turns squared and the permeability of the core material. This relationship can be derived from the concept of magnetic field energy stored in the coil. When a current flows through a coil, it creates a magnetic field, which stores energy. The magnetic field energy is proportional to the square of the current, the number of turns, and the permeability of the core material. The self-inductance of the coil is defined as the ratio of the magnetic field energy to the square of the current, and therefore, it depends on the number of turns and the permeability of the core material.
8. How does the mutual inductance between two coils depend on the number of turns, the relative orientation of the coils, and the permeability of the medium between them? Explain using the concept of magnetic flux linkage and the formula for mutual inductance.
Answer: The mutual inductance between two coils is directly proportional to the square root of the product of the number of turns in each coil, the relative orientation of the coils, and the permeability of the medium between them. This relationship can be understood by considering the concept of magnetic flux linkage. When a changing current flows through one coil, it creates a changing magnetic field, which induces an emf in the other coil. The magnitude of this induced emf depends on the rate of change of magnetic flux linkage, which is determined by the number of turns, the relative orientation, and the permeability of the medium. The mutual inductance is defined as the ratio of the induced emf to the rate of change of current, and therefore, it depends on these factors.
9. How does the energy stored in an inductor depend on the inductance and the current flowing through it? Explain using the concept of magnetic field energy and the formula for energy stored in an inductor.
Answer: The energy stored in an inductor is directly proportional to the square of the inductance and the square of the current flowing through it. This relationship can be derived from the concept of magnetic field energy stored in the inductor. When a current flows through an inductor, it creates a magnetic field, which stores energy. The magnetic field energy is proportional to the square of the current and the inductance. Therefore, the energy stored in an inductor is defined as half the product of the inductance and the square of the current.
10. How does the magnetic field produced by a moving charge depend on its velocity and the distance from the charge? Explain using the Biot-Savart law and the concept of magnetic field lines.
Answer: The magnetic field produced by a moving charge is directly proportional to the velocity of the charge and inversely proportional to the distance from the charge. This relationship can be derived from the Biot-Savart law, which states that the magnetic field produced by a moving charge is directly proportional to the product of the charge, the velocity of the charge, and the sine of the angle between the velocity vector and the line connecting the charge to the point of interest. In the case of a moving charge, the magnetic field lines form concentric circles around the charge, and the density of these lines decreases with increasing distance from the charge. Therefore, the magnetic field strength decreases with increasing distance from the charge.