## Hall Effect Thruster

#### 1. Ampere’s circuital law can only be applied to certain cases. Does it mean that this law is not true in general?

Ampere’s circuital law states that the line integral of the magnetic field around any closed path in free space is equal to 11.0 times the total current enclosed by that path. i.e.

∮Bdl = µoI

This law can only be applied in those situations where it is possible to determine the value of the line integral of B around a closed path. For other situations where no such path is available, Biot-Savart law is used to determine B. But it does not mean that this law is not true in general.

**Note: B and dl are vectors**

#### 2. A slowly moving electron beam gradually diverges but a fast-moving beam gradually converges. Why?

If the electron beam is moving slowly, electrostatic repulsion is greater than the magnetic attraction. So the beam diverges. As the velocity goes on increasing, magnetic attraction increases which dominates the electrostatic repulsion when the beam has a high velocity.

#### 3. What is a toroid?

An endless solenoid in the form o f a ring is called to Toroid as shown in the figure. The magnetic lines of force inside the toroid are circular, concentric with the center of the toroid. The magnetic fitted inside a toroid is uniform because it has no ends.

#### 4. In the Hall effect experiment, how can we make the Hall emf disappear?

If a current-carrying conductor is placed inside a magnetic field, Hall emf is produced. If we move the entire conductor in the opposite direction to the current with a speed equal to the drift speed of electrons, then the electrons are at rest with respect to the magnetic field. Hence the Hall emf disappears. Thus the conductor speed needed to make the Hall emf vanish is equal to the drift speed.

#### 5. What is Hall Effect?

When a magnetic field is applied to a metallic slab carrying current, an emf is set up across the specimen, in the direction perpendicular to both current and the magnetic field. ‘This effect is called the Hall Effect.

#### 6. What is Hall voltage?

The maximum potential difference across the specimen carrying current inside the magnetic field at which the motion of the electrons ceases (electric force is equal to Lorentz force) is called Hall Voltage. When the p.d. reaches the Hall voltage then

Electric force = Lorentz force

or eE = Be v

or VH/d=Bv

or VH = Bvd

Where E is the electric field produced due to Hall Voltage, v is the drift velocity of electron and d is the separation between opposite faces between which Hall Voltage is produced.

#### 7. What are the uses of the Hall effect?

Hall effect becomes apparent when semiconductors are used because Hall voltage is much more measurable in semiconductors than in metals. Apart from its use in semiconductor investigations, a Hall Probe may be used to measure the flux density of a magnetic field.

#### 8. How Hall voltage is produced? Explain. OR Explain how Hall Effect is produced?

If a current I is passed along the +ve X direction in a metallic slab as shown in the figure, the electrons are drifting with velocity v in the negative X direction. When a magnetic field B is applied along +Z direction, Lorentz’s force Fe = Bev acts on each electron along – ve Y-direction.

As a result, the electrons accumulate at the lower surface C & hence this surface appears at a negative potential. Simultaneously a positive potential appears at the upper surface B due to positively charged atoms. Thus a p.d or emf produced between two surfaces produces an electric field thereby creating an electric force Fe=eE along +ve Y-direction on the electrons. By this process, the flow of electrons ceases when the emf between faces B and C reaches a particular value called Hall Voltage VH.

#### 9. What is the difference between Biot Savart’s law and Ampere’s Circuital law?

The major differences between Biot Savart’s law & Ampere’s Circuital law are listed below:

(a) Biot Savart’s law can be used for both symmetrical and anti-symmetrical current distribution. However, ampere circuital law can be used only for symmetrical current distribution.

(b) Magnetic Fields 121 In highly symmetric problems, it is easy to use ampere’s circuital law than Biot Savart’s law.

#### 10. How can the motion of moving charged’ particles be used to distinguish between a magnetic field & an electric field? Give a specific example to justify your argument.

The magnetic force on a moving charged particle is always perpendicular to the direction of motion. There is no magnetic force on a moving charge when it moves in the direction of the magnetic field. On the other hand, the force on an electric charge moving through an electric field is never zero. Therefore, by projecting the particle in different directions, it is possible to determine the nature of the field.

#### 11. Is it possible to orient a current loop is a uniform magnetic field such that the loop will not tend to rotate? Explain.

Yes, it is possible. If the magnetic field is perpendicular to the plane of the loop, the force on opposite sides will be equal and opposite but produce no net torque.

#### 12. What are the similarities between Ampere’s law in magnetism and Gauss’s law in electrostatics?

Both laws are useful for calculating the field of highly symmetric current or charge distribution. Ampere’s law involves a line integral over a closed path through which currents may pass, while Gauss’s law involves a surface integral over a surface that may enclose some net charge.

#### 13. Why is B non zero outside a solenoid? Why is B=0 outside a toroid? (Note that the lines of B must form closed paths)

Since the lines of B must form closed paths, we see that this can only occur if the lines of the solenoid return outside the solenoid. In the case of the toroid, all the closed paths forming the lines of B are contained within the ring.

#### 14. As the conducting bar in the figure moves to the right, an electric field is set up directed downward. If the bar were moving to the left, explain why the electric field would be upward?

If the bar were moving to the left the magnetic force on the negative charge carrier in the bar would act upward causing an accumulation of negative charge at the top & positive at the bottom. Hence the electric field in the bar would be upward.

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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.