#### 1. State Biot-Savart law or Laplace’s law.

Biot-Savart law states that the magnetic field produced due to a small conductor of length dl carrying a current I at a point at a distance r is given by

dB = μo/4π[Idlsinθ/r^2]

where θ is the angle between the direction of flow of current and the line joining the small conductor to the observation point.

#### 2. Define one tesla.

The Lorentz’s force on a charge q moving with velocity v, making an angle 0 with magnetic field B is given by F = Bqv sinθ. If F = 1N, q = 1C, v = 1m/s and sin θ = 1, then B = 1 tesla. Hence 1 tesla is defined as the magnetic field intensity at a point if 1C charge moving with a velocity of 1msec-1 at a right angle to the magnetic field exerts one Newton force on the charge.

#### 3. What is the total magnetic field at the center of a circular loop as shown in the figure?

The total magnetic field at the center of a circular coil through which current is flowing as shown in the figure will be zero because through the two halves of the loop the same current flows but in opposite direction. Hence they produce equal magnetic fields but in opposite direction. So they cancel each other.

#### 4. State the rule that is used to find the direction of the magnetic field at a point near a current-carrying straight conductor.

We can use the right-hand thumb rule to find the direction of the magnetic field at a point near a current-carrying straight conductor. This rule states that if a straight current-carrying conductor is held in our right hand so that the thumb shows the direction of the conventional direction of current in the wire, then the direction of the curl of the finger shows the direction of the induced magnetic field.

#### 5. State Ampere’s theorem. [HSEB 2054]

Ampere’s theorem states that the line integral of the magnetic field intensity. B around any close loop in a vacuum is equal to µotimes the total current enclosed by the path where µo is the permeability of a vacuum.

∮B.dl= µoI

and this law is true only for stationary current.

Where I is the current enclosed by the loop. This law relates the magnetic field to the current.

#### 6. Does a charge move along the direction of the magnetic field experience a force?

No, the charge does not experience the magnetic Lorentz force because the force is given by F = Bqvsinθ. Where θ is the angle made by the charge q moving with velocity v with applied magnetic field B. When the charge moves along the magnetic field, θ = 0° and F becomes zero.

#### 7. Can a charged particle move through a magnetic field without experiencing any force? Explain. [HSEB 2072]

Yes, a charged particle can move through a magnetic field without experiencing any force. It happens when it moves parallel to the field since force experienced by a charge (q) moving in a magnetic field of intensity (B) is given by F = Bqv sinθ

Since the charge is moving in a magnetic field neither B nor q nor v can be zero. So to have F zero, either θ = 0° or 180° i.e. the motion of the charge is parallel to the field.

#### 8. Does a stationary charge experience a force in an electric field?

Yes, it experiences an electric Lorentz force which is given by F = qE

Since it is independent of the velocity of the charge. Where E is the strength of the electric field.

#### 9. Does a charged particle moving through a magnetic field experience a force? Express with conditions, maximum and minimum force it experiences. [HSEB 2055]

Yes, it experiences a force which is called **Magnetic Lorentz Force**. It is given by F = Bqv sinθ where B is the magnetic field intensity, q is the charge, v is the velocity of the charge and θ is the angle between the direction of v and B. Hence it will be maximum when θ = 90° and maximum force is given by Fmax = Bqv sin 90° i.e. Fmax = Bqv. It will be minimum when θ = 0° and minimum force is given by Fmin = Fqv sin 0° = 0.

#### 10.An electron is not deflected while moving through a certain region of space. Can we be sure that there is no magnetic field in the region?

When an electron moves through a certain region and if it is not deflected, then either there may not be a magnetic field or there may be a magnetic field in the direction parallel to the direction of motion of the electron. So we can not be sure that there is no magnetic field in the region.

#### 11. In a field, the force experienced by a charge depends only upon the magnitude of the field and does not depend upon the velocity. Is the field electric or magnetic in nature?

If the force experienced by a charge depends upon the magnitude of charge (q) but not on the velocity (v), then it is an electrostatic field and the force is electric Lorentz force since it is given by F = q E. The magnetic Lorentz force is given by F = Bqv sinθ and it depends upon the velocity.

#### 12. Free electrons always keep on moving in a conductor. But no force acts on them in a magnetic field unless a current is passed through it. Why?

In the absence of an electric current, due to the random motion of electrons, they do not have velocity in any particular direction. We know that the magnetic Lorentz force also depends on the velocity, they do not experience any force. But as the current is passed through the conductor, electrons get velocity in a particular direction and they experience magnetic Lorentz force which is given by F = B qv sin**θ** where the symbols have their usual meaning.

#### 13. A proton moving in a straight line enters a strong magnetic field along the field direction. How will its path and velocity change? [HSEB 2057]

When a proton moving in a straight line enters a strong magnetic field along the field direction, it does not experience any magnetic Lorentz force since it is given by F = Bqv sinθ and here θ = 0°. So it will not change its path as well as its velocity.

#### 14. Why do two straight parallel metallic wires carrying current in the opposite direction repel each other?

When two straight parallel metallic wires carrying currents I1 and 12 respectively in the opposite direction are separated at a perpendicular distance r, one lies in the magnetic field produced by the another. So both of them experience the magnetic Lorentz force which tries to bring them away from each other. The force experienced is given by F = μoI1I2/2**π**r

#### 15. Does the magnetic Lorentz force does work on the moving charge in the magnetic field?

The magnetic Lorentz force experienced by a moving charge (q) with a velocity ( v ) in a magnetic field intensity ( B ) is given by F =q (v x B )

This shows that the direction of this force is perpendicular to v and B both. i.e. the angle between force and velocity is 90°. The direction of velocity is in the direction of displacement. Therefore, the angle between force and displacement (d) is also 90°. We know

Work = Fd cos 0 = Fd cos 90° i.e. Work = 0

Hence it does not do any work on the moving charge.

#### 16. When a charge moves in a magnetic field, its velocity or K.E remains unchanged. Explain, why?

When a charge moves in a magnetic field, it experiences the magnetic Lorentz force which is given by F = q( v x B ). This force is perpendicular to both the velocity ( v ) of the charge (q) and the magnetic flux density (B ). Hence the component of force along the direction becomes F cos 90° = 0. Since the force has no effect along the direction of velocity, it has no effect on the magnitude of v keeping the K.E. of the charge constant.

#### 17. What is a solenoid?

A solenoid is a circular coil of a large number of turns, such that the turns of the solenoid run parallel to its length. The length of the solenoid is much larger than its diameter. When a current is passed through the solenoid, the same current passes through each turn and produces a uniform magnetic field inside it. The magnetic field produced by the solenoid inside it is given by B =µonI. When n is the number of turns per unit length.

#### 18. Why does a current-carrying solenoid try to contract? [HSEB 2067]

#### OR A current was sent through a dual coil spring. The spring contracted as if it had been compressed. Why? [HSEB 2071]

When current is passed through a solenoid, current in the various turns of the solenoid is parallel and in the same direction. So the parallel wires which have current in the same direction experience the force towards each other and they try to contract.

#### 19. Why is the cylindrical core of soft iron used in the moving coil galvanometer? [HSEB 20601

#### OR What is the main function of soft iron core used in a moving coil meter?

When a soft iron core is used, the magnetic lines of force tend to crowd through the core which increases the strength of the magnetic field. It increases the sensitivity of the moving coil meter. It also helps to make the magnetic field radial which makes the torque on the coil uniform.

#### 20. How is the magnetic field made radial in a moving coil galvanometer? [HSEB 2061]

To make the magnetic field radial in a moving coil galvanometer, a bar magnet with concave poles is used, and also the soft iron Core is used to make the magnetic field more radial.

#### 21. What is the importance of the radial magnetic field in the moving galvanometer?

g coil When the magnetic field is made radial, the normal to the plane of and the direction of the magnetic field becomes always 90° which makes the torque on the coil maximum and uniform. If we had used the magn e which has flat poles, the torque on the coil would decrease as it rotates from its equilibrium position.

#### 22. In what way is an electric field different from a magnetic field?

An electric field exerts a force on a charged particle whether it is in motion er not which is known as electric Lorentz force. It changes the kinetic energy of the charge. But the magnetic field exerts the magnetic Lorentz force on the charge only if it is in motion and the motion is not parallel to the magnetic field. This force does not change the kinetic energy of the charge since this forte is perpendicular to the direction of the velocity. It changes the direction of velocity only.

#### 23. Under what conditions does a charge affect a magnet? [HSEB 2054]

If the charge is at rest, it does not produce a magnetic field. When the charge moves, it produces the magnetic field around it. If a magnet is placed inside its magnetic field, it affects the magnet due to the magnetic field induced by it.

#### 24. An electron beam is deflected in the uniform field. How do you know whether the field is electric or magnetic?

An electron beam in the uniform electric field moves in a parabolic path while it moves along a circular path in the uniform magnetic field. So if the path of the beam is parabolic, the field is electric and it is magnetic if the path is circular.

#### 25. What is the nature of the magnetic field on the center of a circular loop carrying current?

When a current is passed through a circular loop, a magnetic field is produced in a plane perpendicular to the circular loop. Near the edges, the magnetic lines of force are circular while near the center they are parallel as shown in the figure. The direction of the magnetic field is given by the right-hand fist rule.

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Niraj Raut is the CEO of Merocourse and writes blog posts for Ignited Nepal, Merocourse, and ProtoTrend. He studied B.Sc.CSIT at Tribhuvan University.