The flux density through a Hall probe doubles, with the same current. What happens to the Hall voltage?

It doubles. The Hall voltage is proportional to B.

In a velocity selector, what is the speed of the particles that pass straight through?

E ÷ B. The electric force qE balances the magnetic force Bqv.

Why is the slice in a Hall probe made very thin?

A thinner slice gives a bigger Hall voltage. The Hall voltage is proportional to 1 ÷ t.

When the Hall voltage is steady, what balances the magnetic force on the charge carriers?

the electric force from the charge that has built up. That is why no more charge moves across.

What is a Hall probe used to measure?

magnetic flux density. Its Hall voltage is proportional to B.

The Hall effect and velocity selection · Cambridge A Level Physics

In plain words

Pass a current along a thin slice of semiconductor, put it in a magnetic field, and a small voltage appears across the slice from side to side. The field has shoved the moving charges towards one edge. That voltage is the Hall voltage, and it gives a simple way of measuring a magnetic field.

4 things to know

How it arises: the charge carriers moving through the slice feel a magnetic force that pushes them to one side. Charge builds up there and sets up an electric field across the slice. It builds until the electric force on the carriers balances the magnetic force: qE = Bqv. The steady p.d. across the slice is the Hall voltage.
Hall voltage = BI ÷ ntq, where n is the number of charge carriers per unit volume, t is the thickness of the slice (measured along the field) and q is the charge on each carrier.
A Hall probe uses this to measure flux density: with a steady current, the Hall voltage is proportional to B. The slice must be at right angles to the field. A semiconductor is used because its n is small, which makes the Hall voltage big enough to measure.
Velocity selection: a beam of charged particles passes through an electric field and a magnetic field at right angles to each other and to the beam. Only particles for which the two forces balance, qE = Bqv, go straight through. Their speed is v = E ÷ B.

Worked example

A Hall probe has a slice 0.50 mm thick with 2.0 × 10²² charge carriers per m³, each of charge 1.60 × 10⁻¹⁹ C. It carries 50 mA in a field of flux density 0.20 T. Find the Hall voltage.

Hall voltage = BI ÷ ntq.
= 0.20 × 0.050 ÷ (2.0 × 10²² × 0.50 × 10⁻³ × 1.60 × 10⁻¹⁹).
= 0.010 ÷ 1.6 = 6.3 × 10⁻³ V (6.3 mV).

Tips and tricks

To derive the formula: qE = Bqv, with E = (Hall voltage) ÷ width, and I = nAvq, with A = width × thickness.
A smaller n or a thinner slice gives a bigger Hall voltage.

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

The Hall effect and velocity selection: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

The flux density through a Hall probe doubles, with the same current. What happens to the Hall voltage?
- It doubles. (the answer)
- It halves.
- It stays the same.
- It becomes four times bigger.
The Hall voltage is proportional to B.
In a velocity selector, what is the speed of the particles that pass straight through?
- E ÷ B (the answer)
- B ÷ E
- EB
- E²B
The electric force qE balances the magnetic force Bqv.
Why is the slice in a Hall probe made very thin?
- A thinner slice gives a bigger Hall voltage. (the answer)
- A thinner slice is stronger.
- A thinner slice carries more current.
- A thinner slice has more charge carriers.
The Hall voltage is proportional to 1 ÷ t.
When the Hall voltage is steady, what balances the magnetic force on the charge carriers?
- the electric force from the charge that has built up (the answer)
- their weight
- friction
- nothing
That is why no more charge moves across.
What is a Hall probe used to measure?
- magnetic flux density (the answer)
- electric current
- temperature
- capacitance
Its Hall voltage is proportional to B.

5 questions

Tap an answer and you’ll see straight away whether it’s right, and why.

Worksheet

3 questions, 7 marks. Write your answers on paper, then check them.

The Hall effect and velocity selection

Cambridge International AS & A Level Physics 9702 · 7 marks · papermunch.org

Name ______________________________ Date ______________

Explain how a Hall voltage arises.[3]
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The moving charge carriers feel a magnetic force that pushes them towards one side of the slice. Charge builds up on that side, producing an electric field across the slice. The build-up continues until the electric force on the carriers equals the magnetic force, leaving a steady p.d. across the slice.
I got this one
A velocity selector has an electric field of 3.0 × 10⁴ V/m and a magnetic field of flux density 0.015 T. Find the speed of the particles that pass straight through.[2]
Show answerHide answer
2.0 × 10⁶ m/s.
I got this one
Explain why a Hall probe is made from a semiconductor rather than a metal.[2]
Show answerHide answer
A semiconductor has far fewer charge carriers per unit volume, so for the same current they move faster and the Hall voltage is much larger and easier to measure.
I got this one

Answers: The Hall effect and velocity selection

1. The moving charge carriers feel a magnetic force that pushes them towards one side of the slice. Charge builds up on that side, producing an electric field across the slice. The build-up continues until the electric force on the carriers equals the magnetic force, leaving a steady p.d. across the slice.
2. 2.0 × 10⁶ m/s.
3. A semiconductor has far fewer charge carriers per unit volume, so for the same current they move faster and the Hall voltage is much larger and easier to measure.