Magnetic Fields (Edexcel A Level Physics)

Topic Questions

2 marks

Tiny sensors in smartphones could be used to determine the position of the phone on the Earth’s surface by measuring the Earth’s magnetic flux density.

A current $I$ and a magnetic field of flux density B are applied to a slice of semiconductor as shown. The slice has thickness t and depth d.

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Electrons collect at the top edge of the slice and the bottom edge becomes positively charged. As a result a potential difference known as a Hall voltage V_HALL, develops.

Explain why electrons will collect at the top edge of the slice.

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1b1 mark

Add to the diagram to show clearly two points between which V_HALL, develops.

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4 marks

Electrons continue to collect at the top edge of the slice, until the force on a moving electron due to the magnetic field is equal to the force on the electron due to the electric field.

Derive the following equation for V_HALL:

V_{H A L L} = \frac{B I}{n t e}

where n is the number of charge carriers per unit volume of the semiconductor.

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3 marks

Show that the units are the same on each side of the equation

V_{H A L L} = \frac{B I}{n t e}

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2 marks

The table gives the values of n and t for a number of material samples.

material	n / m^-3	t / m
copper	8.47 x 10²⁸	110 x 10^-6
germanium	2.25 x 10¹⁹	1.10 x 10^-6
silicon	1.44 × 10¹⁶	120 x 10^-6

Deduce which sample would result in the largest Hall voltage for a particular current and magnetic field.

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2 marks

Two sensors in the smartphone were used to determine the horizontal component B_H, and the vertical component B_Vof the Earth’s magnetic flux density.

Calculate the angle of the Earth’s magnetic field to the horizontal.

B_H = 19.0 µT

B_V= 49.0 µT

Angle = .....................................

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3 marks

A student set up the apparatus shown. A length of rigid wire was held horizontally by a clamp in a uniform magnetic field of flux density B.

The circuit connected to the rigid wire is also shown.

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With the switch open, the balance was set to zero. When the switch was closed a current $I$ in the circuit was recorded by the ammeter and the reading on the balance increased.

The length $l$ of wire in the magnetic field was 15.5 cm. When the current in the circuit was 4.55 A, the reading on the balance increased by 5.65 g.

Calculate the magnetic flux density B in the region of the rigid wire.

B = .......................................................

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3 marks

The student wrote the following statement

“The balance could read to the nearest 0.01 g, which makes my values for the magnetic force both accurate and precise.”

Comment on this statement.

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7 marks

At the end of the 19th century, J.J. Thompson used electric and magnetic fields to deflect beams of charged particles. A photograph of his apparatus is shown.

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Electrons were accelerated through a potential difference to produce a beam of high-energy electrons. The beam was then deflected in perpendicular directions by the magnetic and electric fields. The final position of the beam on the screen was determined by the charge and mass of the electrons.

Explain how electrons from the source become a beam of high-energy electrons.

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4 marks

An electron is travelling left to right and enters a region of uniform magnetic field as shown below. The direction of the magnetic field is perpendicular to the direction of travel of the electron.

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The magnetic field deflects the electron in the direction up the page.

Explain the direction of the magnetic field that would produce this deflection.

(2)

ii)

Explain why the electron would travel in a circular path if no other forces acted on it.

(2)

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5 marks

In a modern version of Thompson’s experiment, a uniform electric field of electric field strength E is applied so that the electric and magnetic forces on the electrons are equal and in opposite directions.

Show that for electrons to be undeflected their velocity must be given by

$v = \frac{E}{B}$

where B is the magnetic flux density of the magnetic field.

(2)

ii)

The beam is produced by accelerating electrons through a potential difference of 250 V. The electric field strength is 1.4 × 10⁴ V m⁻¹. The magnetic flux density is 1.5 × 10⁻³ T.

Calculate the value of the specific charge e/m for the electron using this data.

(3)

e/m = ...................................

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1 mark

In his original experiments, Thompson determined the specific charge of a range of particles. His results indicated that the specific charge of an electron is about 2000 times bigger than that for a hydrogen ion.

Deduce what conclusion can be made from this information.

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