Cambridge AS & A Level9702

Magnetic fields

Physics 9702 Chapter Notes

What this chapter covers

Magnetic fields - Concept of a magnetic fieldMagnetic fields - Force on a current-carrying conductorMagnetic fields - Force on a moving chargeMagnetic fields - Magnetic fields due to currentsMagnetic fields - Electromagnetic induction
ShareWhatsAppPost
Magnetic fields notes

Unable to load PDF

The notes viewer could not load. Please refresh the page.

Read online free. Download a watermarked copy with a free account.

Read the notes

The full Magnetic fields notes as text: skim, search, and jump between subtopics.

~13 min read

In this chapter

  1. 1Magnetic Fields and Field Lines
  2. 2Force on a Current-Carrying Conductor
  3. 3Calculating the Magnetic Force
  4. 4Defining Magnetic Flux Density (B)
  5. 5Forces Between Parallel Currents

1. Magnetic Fields and Field Lines

A magnetic field is a region in space where a magnetic pole or a moving electric charge experiences a force. These fields are produced either by permanent magnets or by electric currents (moving charges). We visualize magnetic fields using magnetic field lines. These lines show the direction and strength of the field. The direction of a field line at any point is the direction a 'free' north pole would move if placed there, so lines always point from a north pole to a south pole. The closer the lines are together, the stronger the magnetic field. For currents, we can use the Right-Hand Grip Rule: if you point your thumb in the direction of the conventional current, your fingers curl in the direction of the magnetic field lines. This applies to a straight wire (concentric circles), a flat coil, and a solenoid (a long coil). The field inside a long solenoid is strong and almost uniform. Placing a soft iron core inside a solenoid concentrates the field lines, making the electromagnet much stronger.

Key term

Magnetic Field Line: An imaginary line used to represent a magnetic field, where its direction indicates the direction of the force on a north pole and its density indicates the field's strength.

Examiner insight

Examiners expect clear, non-overlapping field lines with correct direction arrows. For solenoids, showing both the internal uniform field and the external looping field is crucial for full marks.

Common pitfall

Confusing the Right-Hand Grip Rule (for finding the direction of the field created by a current) with Fleming's Left-Hand Rule (for finding the force on a current in a field).

Fun fact

Earth's magnetic field, which acts like a giant bar magnet, is generated by electric currents in its molten outer core. This field protects us from harmful solar wind.

Worked example 13 marks

Sketch the magnetic field pattern for a long solenoid with a current flowing as shown. Indicate the North and South poles.

  1. 1

    Step 1: Use the Right-Hand Grip Rule. Curl the fingers of your right hand in the direction of the current flowing around the coil.

  2. 2

    Step 2: Your thumb points to the left. This indicates that the left end of the solenoid is the North pole.

  3. 3

    Step 3: The right end of the solenoid is therefore the South pole.

  4. 4

    Step 4: Draw field lines emerging from the North pole (left end) and entering the South pole (right end). The lines should loop around the outside from left to right.

  5. 5

    Step 5: Inside the solenoid, draw straight, parallel, and evenly spaced field lines pointing from South to North (from right to left), indicating a strong, uniform field.

Recap

  • Magnetic fields are regions of force created by magnets or moving charges.
  • Magnetic field lines show the direction (North to South) and strength (line density) of a field.
  • The Right-Hand Grip Rule determines the field direction for a current-carrying wire.
  • A solenoid's magnetic field is similar to a bar magnet's and is uniform inside.
  • A ferrous (iron) core significantly strengthens a solenoid's magnetic field.

Quick check

  1. A straight vertical wire carries a current downwards. What is the direction of the magnetic field at a point to the east of the wire?1 mark

2. Force on a Current-Carrying Conductor

When a wire carrying an electric current is placed in an external magnetic field, it experiences a force. This is known as the motor effect. The force arises because the magnetic field from the current interacts with the external magnetic field. The two fields combine, creating a region of stronger field on one side of the wire and a weaker field on the other. The wire is pushed from the stronger field region to the weaker one. The direction of this force can be predicted using Fleming's Left-Hand Rule. Hold your left hand with your thumb, first finger, and second finger all at 90 degrees to each other. Your First finger points in the direction of the external magnetic Field (North to South). Your seCond finger points in the direction of the conventional Current. Your ThuMb will then point in the direction of the resulting Force (or Motion).

Key term

Motor Effect: The phenomenon where a force is exerted on a current-carrying conductor when it is placed in a magnetic field.

Examiner insight

Marks are often awarded for explicitly stating Fleming's Left-Hand Rule before applying it. Be clear and methodical in your application of the rule in exam answers.

Common pitfall

Using the right hand instead of the left hand for the motor effect, or pointing the 'Current' finger in the direction of electron flow instead of conventional current.

Worked example 12 marks

A horizontal wire is placed in a uniform magnetic field that is directed vertically downwards. The current in the wire flows from East to West. Determine the direction of the force on the wire.

  1. 1

    Step 1: Identify the directions for Fleming's Left-Hand Rule.

  2. 2

    Step 2: Point your First finger (Field) downwards, as the magnetic field is directed downwards.

  3. 3

    Step 3: Point your seCond finger (Current) in the direction of the current, which is from East to West.

  4. 4

    Step 4: Observe the direction your ThuMb (Force/Thrust) is pointing. It will be pointing towards the North.

  5. 5

    Step 5: Therefore, the force on the wire is directed North.

Recap

  • A current in a magnetic field experiences a force (the motor effect).
  • The force is due to the interaction between the external field and the current's own field.
  • Fleming's Left-Hand Rule determines the direction of the force.
  • First finger = Field, seCond finger = Current, ThuMb = Thrust/Force.
  • Remember to use the direction of conventional current (+ to -).

Quick check

  1. What three quantities are represented by the thumb, first finger, and second finger in Fleming's Left-Hand Rule?2 marks

3. Calculating the Magnetic Force

The magnitude of the force on a straight conductor in a uniform magnetic field depends on the strength of the field, the current in the wire, and the length of the wire within the field. This relationship is given by the equation F = BIL sin(θ). Here, F is the force in newtons (N), B is the magnetic flux density in tesla (T), I is the current in amperes (A), and L is the length of the conductor inside the field in metres (m). The term θ is the angle between the conductor and the magnetic field lines. The force is at its maximum when the wire is perpendicular to the field (θ = 90°, sin(90°) = 1), so the formula simplifies to F = BIL. The force is zero when the wire is parallel to the field (θ = 0°, sin(0°) = 0), as the wire is not 'cutting' any field lines.

F = BIL sin(θ)

Key term

Angle θ: In the equation F = BIL sin(θ), θ is the angle between the direction of the current and the direction of the magnetic field.

Examiner insight

Examiners look for the correct formula, correct substitution with units converted, and the final answer to an appropriate number of significant figures. Show your working clearly.

Common pitfall

Forgetting to convert length from centimetres to metres before substituting into the formula, or failing to use the sin(θ) term when the angle is not 90°.

Worked example 13 marks

A straight wire of length 50 cm carries a current of 2.5 A. It is placed in a uniform magnetic field of magnetic flux density 0.040 T. The wire is at right angles to the field. Calculate the magnitude of the force on the wire.

  1. 1

    Step 1: Identify the known variables. L = 50 cm = 0.50 m, I = 2.5 A, B = 0.040 T.

  2. 2

    Step 2: The wire is at right angles to the field, so θ = 90° and sin(θ) = 1. The formula simplifies to F = BIL.

  3. 3

    Step 3: Substitute the values into the formula: F = 0.040 T × 2.5 A × 0.50 m.

  4. 4

    Step 4: Calculate the result: F = 0.050 N.

Worked example 23 marks

A 15 cm length of wire carrying a 4.0 A current is at an angle of 30° to a uniform magnetic field of flux density 0.25 T. Calculate the force on the wire.

  1. 1

    Step 1: Identify the known variables. L = 15 cm = 0.15 m, I = 4.0 A, B = 0.25 T, θ = 30°.

  2. 2

    Step 2: Use the full formula F = BIL sin(θ) as the wire is not perpendicular to the field.

  3. 3

    Step 3: Substitute the values: F = 0.25 T × 4.0 A × 0.15 m × sin(30°).

  4. 4

    Step 4: Calculate the result: F = 0.25 × 4.0 × 0.15 × 0.5 = 0.075 N.

Recap

  • The magnetic force is calculated using F = BIL sin(θ).
  • Force is maximum when the conductor is perpendicular (90°) to the field.
  • Force is zero when the conductor is parallel (0°) to the field.
  • Ensure all quantities are in SI units before calculating: metres, amperes, tesla.
  • The 'L' in the formula is only the length of the wire that is actually inside the magnetic field.

Quick check

  1. If you double the current in a wire that is perpendicular to a magnetic field, what happens to the magnitude of the force on it?1 mark

4. Defining Magnetic Flux Density (B)

Magnetic flux density, symbol B, is the quantitative measure of the strength of a magnetic field. It is a vector quantity, having both magnitude and direction. We can define it formally using the motor effect equation. If we rearrange F = BIL for a wire at 90 degrees to the field, we get B = F / (IL). From this, we can define magnetic flux density as the force experienced per unit current per unit length on a straight conductor placed perpendicular to the magnetic field. The SI unit for magnetic flux density is the tesla (T). One tesla is a very strong magnetic field; it is defined as the magnetic flux density that produces a force of 1 newton on a 1 metre length of wire carrying a 1 ampere current at right angles to the field. Therefore, 1 T = 1 N A⁻¹ m⁻¹.

B = F / (I L)

Key term

Magnetic Flux Density (B): The force experienced per unit current per unit length on a straight conductor placed at right angles to a uniform magnetic field.

Examiner insight

A precise, word-for-word definition of magnetic flux density is a common exam question. Memorise it, ensuring you include the 'perpendicular' condition.

Common pitfall

Stating the definition of magnetic flux density without specifying the condition that the conductor must be 'perpendicular' or 'at right angles' to the field.

Fun fact

The most powerful man-made magnetic fields, created using pulsed magnets, can exceed 1000 T for a few milliseconds, but this is enough to rip most materials apart.

Worked example 13 marks

A 12 cm long conductor carrying a current of 5.0 A experiences a force of 0.030 N when placed perpendicular to a uniform magnetic field. Calculate the magnetic flux density of the field.

  1. 1

    Step 1: State the formula for magnetic flux density, B = F / (IL).

  2. 2

    Step 2: Identify the given values and convert to SI units. F = 0.030 N, I = 5.0 A, L = 12 cm = 0.12 m.

  3. 3

    Step 3: Substitute the values into the formula: B = 0.030 N / (5.0 A × 0.12 m).

  4. 4

    Step 4: Calculate the result: B = 0.030 / 0.60 = 0.050 T.

  5. 5

    Step 5: The magnetic flux density is 0.050 T or 50 mT.

Recap

  • Magnetic flux density (B) is a measure of magnetic field strength.
  • It is defined by the equation B = F / (IL) for a perpendicular conductor.
  • The SI unit for magnetic flux density is the tesla (T).
  • One tesla is equal to one newton per ampere-metre (1 T = 1 N A⁻¹ m⁻¹).
  • A larger value of B indicates a stronger magnetic field.

Quick check

  1. State the definition of the tesla.2 marks

5. Forces Between Parallel Currents

Since a current-carrying wire produces its own magnetic field, two parallel current-carrying wires will interact. Each wire sits in the magnetic field of the other, and so each experiences a force. We can work out the direction of this force. Consider two wires with currents in the same direction. Wire 1 creates circular magnetic field lines around it (Right-Hand Grip Rule). At the position of Wire 2, this field is directed into the page. Now use Fleming's Left-Hand Rule on Wire 2: Field is into the page, Current is upwards. The resulting force (Thumb) is towards Wire 1. By symmetry, the force on Wire 1 is towards Wire 2. Therefore, parallel currents in the same direction attract. If the currents are in opposite directions, the field from Wire 1 is still into the page at Wire 2, but the current in Wire 2 is now downwards. Using the Left-Hand Rule, the force on Wire 2 is now away from Wire 1. Therefore, parallel currents in opposite directions repel.

Key term

Electromagnetism: The principle that moving electric charges create magnetic fields, and that these fields can exert forces on other moving charges.

Examiner insight

Examiners often ask for an explanation of the force between wires, not just the direction. A complete answer involves describing the field produced by one wire and then the force exerted on the second wire.

Common pitfall

Applying electrostatic logic ('like repels') to currents. For parallel currents, 'like' directions attract and 'opposite' directions repel.

Worked example 14 marks

Two long, parallel, vertical wires, P and Q, are placed next to each other. Wire P carries a current upwards, and wire Q carries a current downwards. Do the wires attract or repel? Explain your reasoning.

  1. 1

    Step 1: State the rule for forces between currents. Wires with currents in opposite directions repel each other.

  2. 2

    Step 2: Explain the reasoning. Wire P produces a magnetic field. At wire Q, use the Right-Hand Grip Rule on wire P: the field is directed into the page.

  3. 3

    Step 3: Now consider the force on wire Q. Use Fleming's Left-Hand Rule on wire Q.

  4. 4

    Step 4: Field (First finger) is into the page. Current (seCond finger) is downwards.

  5. 5

    Step 5: The Thumb (Force) points away from wire P, to the right. Therefore, wire Q is repelled by wire P.

  6. 6

    Step 6: By Newton's third law, wire P experiences an equal and opposite force, so it is also repelled from wire Q.

Recap

  • Two parallel current-carrying wires exert a magnetic force on each other.
  • This is because each wire is in the magnetic field created by the other.
  • Currents flowing in the same direction cause the wires to attract.
  • Currents flowing in opposite directions cause the wires to repel.
  • The direction of the force can be deduced by combining the Right-Hand Grip Rule and Fleming's Left-Hand Rule.

Quick check

  1. Two parallel conductors are carrying currents in the same direction. Do they attract or repel?1 mark

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. Define magnetic flux density and state its SI unit.2 marks
  2. A straight, horizontal copper rod is in a uniform magnetic field. The rod is 25 cm long and carries a current of 5.0 A. The magnetic field has a flux density of 0.80 T and is directed vertically. Calculate the magnitude of the force on the rod.3 marks
  3. Sketch the magnetic field pattern produced by a flat, circular coil carrying a current. Your diagram should include the direction of the current and the direction of the magnetic field lines.3 marks
  4. Explain, with the aid of Fleming's Left-Hand Rule, why a current-carrying wire placed in a magnetic field experiences a force.4 marks
  5. A small, straight piece of wire of length 4.0 cm is placed in the uniform field between the poles of a strong magnet, with a flux density of 1.2 T. When a current of 3.0 A flows through the wire, it experiences a force of 0.10 N. Calculate the angle between the wire and the magnetic field lines.4 marks
  6. Explain why two parallel wires carrying currents in the same direction attract each other. You may wish to draw a diagram to support your answer.4 marks
  7. A rectangular coil of wire with 50 turns, dimensions 5.0 cm by 8.0 cm, is suspended in a uniform magnetic field of flux density 0.075 T. The field is parallel to the 5.0 cm sides. If the coil carries a current of 2.0 A, calculate the maximum torque acting on the coil.5 marks
  8. The unit of magnetic flux density, the tesla (T), can be expressed in terms of base SI units (kg, s, A). Show that 1 T is equivalent to 1 kg s⁻² A⁻¹.3 marks
  9. A rigid copper wire is formed into a U-shape and pivoted at its ends so it can swing freely. The lower section of the U, which has a length of 10 cm, passes through a uniform magnetic field of flux density B, directed into the page. When a current of 4.0 A flows, the wire swings to an angle of 15° to the vertical. The mass of the lower section is 5.0 g. Calculate the magnetic flux density B.6 marks
  10. Describe an experiment to determine the magnetic flux density of a uniform magnetic field using a current balance (or top-pan balance). Your description should include the measurements you would take and how you would use them to obtain a value for B.5 marks

Go deeper

Practise and revise with member-only material for this chapter.

Workbook

Exam-style practice questions with full worked solutions.

Unlock with a plan

Chapter at a Glance

A single-page summary of every key idea for fast revision.

Unlock with a plan

Free notes are just the start.

Unlock every Workbook and Chapter at a Glance, and generate your own worksheets and predicted papers.

Explore plans

Related chapters

Physical quantities and unitsKinematicsDynamicsForces, density and pressureWork, energy and powerDeformation of solids