1.
A proton enters a magnetic field of 1.5 T with a velocity of $2 \times 10^7$ m/s at an angle of 30° to the field. Calculate the magnitude of the magnetic force acting on it. ($q_p = 1.6 \times 10^{-19}$ C)
2.
Calculate the magnetic force on a 5 C charge moving with a velocity of $3 \times 10^6$ m/s perpendicular to a uniform magnetic field of 2 T.
3.
An $\alpha$-particle and a proton moving with the same speed enter a uniform magnetic field perpendicularly. Find the ratio of the radii of their circular paths.
4.
An electron moving at $10^7$ m/s experiences a maximum magnetic force of $3.2 \times 10^{-13}$ N. Find the magnitude of the magnetic field.
5.
Find the radius of the circular path of an electron moving at $3 \times 10^6$ m/s in a magnetic field of 0.3 T perpendicular to its velocity. ($m_e = 9.1 \times 10^{-31}$ kg)
6.
Calculate the cyclotron frequency of a proton in a uniform magnetic field of 1 T. (Mass of proton = $1.67 \times 10^{-27}$ kg)
7.
A proton has a kinetic energy of 1 MeV. It moves in a circular path in a uniform magnetic field of 1.5 T. Find the magnetic force acting on it.
8.
Define Lorentz force. Write its complete mathematical expression in vector notation.
9.
An electron moves with velocity $v = 2 \times 10^5$ m/s at an angle of 60° with a uniform magnetic field of 0.5 T. Calculate the pitch of its helical path.
10.
Calculate the time period of revolution of an electron moving in a plane perpendicular to a uniform magnetic field of 0.5 T.
11.
State Biot-Savart Law and express it in vector form. Identify all the terms used.
12.
A long straight wire carries a current of 35 A. What is the magnitude of the magnetic field $\vec{B}$ at a distance of 20 cm from the wire?
13.
Calculate the magnetic field at the center of a circular coil of 100 turns, radius 10 cm, carrying a current of 5 A.
14.
Find the current required in a circular loop of radius 5 cm to produce a magnetic field of $4 \times 10^{-5}$ T at its center.
15.
The magnetic field at a distance of 10 cm from a long straight current-carrying wire is $2 \times 10^{-5}$ T. Calculate the current flowing in the wire.
16.
A straight wire is bent into a semicircle of radius $R$. If it carries a steady current $I$, write the expression for the magnetic field at the center of curvature.
17.
Two concentric circular loops of radii 5 cm and 10 cm carry currents of 2 A and 4 A respectively in the same direction. Find the net magnetic field at their common center.
18.
A very long straight wire carries a current of 50 A. At what distance from the wire will the magnetic field be $10^{-4}$ T?
19.
Two identical circular loops, P and Q, each of radius $R$ and carrying currents $I$ and $2I$ respectively, are lying in parallel planes. Find the ratio of their magnetic fields at their respective centers.
20.
The magnetic field at the center of a circular coil of 1 turn is $B$. If the same wire is rewound into a coil of 2 turns, what will be the new magnetic field at the center for the same current?
21.
State Ampere’s Circuital Law mathematically and define the terms used in the expression.
22.
An ideal solenoid of length 0.5 m has a radius of 1 cm and is made up of 500 turns. It carries a current of 5 A. What is the magnitude of the magnetic field inside the solenoid?
23.
A solenoid 1 m long has 2000 turns. If the magnetic field inside the solenoid is $8\pi \times 10^{-3}$ T, calculate the current flowing through it.
24.
A toroid has a core of inner radius 20 cm and outer radius 22 cm, around which 5000 turns of wire are wound. If the current is 10 A, find the magnetic field inside the core.
25.
For the ideal solenoid mentioned in Question 22, what would be the magnitude of the magnetic field exactly at one of its open ends?
26.
A solenoid has a core of a material with relative permeability 400. If the current is 2 A and there are 1000 turns per meter, calculate the magnetic field inside the core.
27.
A long straight solid cylindrical wire of radius $R = 2$ cm carries a steady current of 2 A distributed uniformly over its cross-section. Calculate the magnetic field at a distance of 1 cm from its axis.
28.
For the same solid cylindrical wire described in Question 27, determine the magnetic field exactly on the surface of the wire.
29.
A toroid has a mean radius of 15 cm and 3000 turns. If the magnetic field inside the toroid is $2 \times 10^{-3}$ T, what is the current flowing through the turns?
30.
A hollow copper pipe carries a steady direct current. Using Ampere's Law, what is the value of the magnetic field inside the hollow portion of the pipe?
31.
Two long parallel wires separated by a distance of 10 cm carry currents of 5 A and 10 A in the same direction. Find the magnitude and nature of the force per unit length between them.
32.
Two straight parallel wires, each 2 m long, are placed 5 cm apart. If they carry a current of 10 A each in opposite directions, calculate the total force acting on each wire.
33.
At what separation distance should two long parallel wires carrying currents of 2 A and 5 A be placed so that the force per unit length between them is exactly $10^{-5}$ N/m?
34.
Find the force acting on a 10 cm long section of a wire carrying 5 A, placed parallel to a long straight wire carrying 20 A at a perpendicular distance of 2 cm.
35.
Write the vector expression for the magnetic force on a straight current-carrying conductor of length vector $\vec{l}$ in a uniform magnetic field $\vec{B}$.
36.
A straight wire of length $L$ carrying current $I$ is placed exactly perpendicular to a uniform magnetic field $B$. What is the magnitude of the force experienced by it?
37.
A straight horizontal conducting wire of mass 20 g and length 50 cm is suspended in a uniform horizontal magnetic field of 0.4 T perpendicular to it. Calculate the current required to make the wire weightless ($g = 10 \text{ m/s}^2$).
38.
Two long parallel wires repel each other with a force $F$ per unit length. If the current in both wires is halved and the distance between them is doubled, what will be the new force per unit length?
39.
State Fleming's Left-Hand Rule used to find the direction of the force acting on a current-carrying conductor placed in a magnetic field.
40.
Three long straight parallel wires A, B, and C are placed in a plane. A and C carry 5 A current in the same direction. If wire B is placed exactly midway between A and C, what is the net magnetic force on wire B?
41.
Calculate the magnetic dipole moment of a circular coil consisting of 50 turns, with a radius of 10 cm, carrying a current of 2 A.
42.
A circular coil of 30 turns and radius 8 cm carrying a current of 6 A is suspended vertically in a uniform horizontal magnetic field of 1.0 T. The field lines make an angle of 60° with the normal to the coil. Calculate the torque.
43.
A square loop of side 10 cm carries a steady current of 5 A. Find the magnitude of its magnetic dipole moment.
44.
A current loop has a magnetic dipole moment of $1.5 \text{ A}\cdot\text{m}^2$. If it is placed in a uniform magnetic field of 0.2 T, what is the maximum torque it can experience?
45.
Calculate the work done required to rotate a magnetic dipole of moment $2 \text{ A}\cdot\text{m}^2$ from a position of stable equilibrium ($0^\circ$) to unstable equilibrium ($180^\circ$) in a magnetic field of 0.5 T.
46.
An electron revolves in a circular orbit of radius 0.5 Å with a frequency of $10^{15}$ Hz. Calculate the equivalent orbital magnetic moment. ($e = 1.6 \times 10^{-19}$ C)
47.
Find the torque acting on a rectangular coil of area $0.01 \text{ m}^2$ with 100 turns, carrying a current of 2 A, when its plane is parallel to a uniform magnetic field of 0.5 T.
48.
In which orientation (angle between the area vector and magnetic field) is the torque on a suspended current loop maximum?
49.
A loop of area $A$ carrying current $I$ has magnetic moment $M$. If the current is halved and the area is doubled, what will be the new magnetic moment?
50.
Calculate the potential energy of a magnetic dipole with moment $M = 0.4 \text{ J/T}$ when it is aligned parallel to a magnetic field $B = 0.16 \text{ T}$.
51.
A galvanometer of resistance $50 \, \Omega$ gives full scale deflection for a current of 2 mA. Calculate the potential difference required across it to produce full scale deflection.
52.
A galvanometer has a coil resistance of $100 \, \Omega$ and a full scale deflection current of 1 mA. Calculate the value of the shunt resistance required to convert it into an ammeter of range 0 to 1 A.
53.
The current sensitivity of a moving coil galvanometer is 5 divisions/mA. If its scale has 50 divisions in total, what is the current required for full scale deflection ($I_g$)?
54.
A galvanometer has a voltage sensitivity of 1 division/V and a coil resistance of $100 \, \Omega$. Calculate its current sensitivity in divisions/A.
55.
A galvanometer with a coil resistance of $15 \, \Omega$ shows full scale deflection for a current of 4 mA. Calculate the series resistance required to convert it into a voltmeter of range 0 to 18 V.
56.
A galvanometer coil has an area of $2 \times 10^{-4} \text{ m}^2$, 100 turns, and is placed in a radial field of 0.1 T. If the torsional constant is $10^{-6} \text{ N}\cdot\text{m/rad}$, find its current sensitivity.
57.
Calculate the total effective resistance of the ammeter formed in Question 52. Is it lower or higher than the original galvanometer resistance?
58.
Calculate the total effective resistance of the voltmeter formed in Question 55. Is it lower or higher than the original galvanometer resistance?
59.
Why are concave pole pieces used to produce a "radial magnetic field" in a moving coil galvanometer?
60.
If the number of turns of a galvanometer coil is doubled (which also roughly doubles its resistance), how does the voltage sensitivity change? Justify.
