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A2 · Practice questions · Magnetic fields and field lines

Lines that show where a compass points.

Six original Cambridge-style questions on magnetic field lines, the patterns around a bar magnet, a straight wire and a solenoid, and adding magnetic fields as vectors.

Original questions All questions on this page are original work, written in the Cambridge AS & A Level style. They are not from past papers. They test the same concepts and skills the syllabus rewards.
Keep these straight

Direction from a compass, strength from the spacing.

01
Analysis
[2 marks]

State what the direction of a magnetic field line represents, and explain why two magnetic field lines can never cross.

  • A field line points in the direction of the force on a north pole, which is the way the north pole of a small compass placed on the line points. ✓
  • At any point the field has a single definite direction; if two lines crossed, a compass there would have to point two ways at once, which is impossible. ✓
02
Calculation
[2 marks]

In a scale drawing of the field near a magnet, the field lines in region P are 4.0 mm apart and in region Q they are 12 mm apart. The flux density in region P is 0.36 T. Estimate the flux density in region Q.

  • In the drawing the number of lines crossing unit length is proportional to the flux density, so B is inversely proportional to the spacing. ✓
  • BQ = 0.36 × (4.0 / 12) = 0.12 T. ✓
03
Calculation
[3 marks]

At a point near a wire the horizontal component of the Earth's magnetic field is 18 μT towards the north, and the field due to the current in the wire is 24 μT towards the east. Calculate the magnitude and direction of the resultant horizontal field, and state the direction in which a compass at the point will settle.

  • The two fields are at right angles and add as vectors: B = √(18² + 24²) = √900 = 30 μT. ✓
  • tan θ = 24 / 18, so θ = 53° east of north. ✓
  • The compass needle lies along the resultant field, so it points 53° east of north. ✓
04
Analysis
[3 marks]

A long straight vertical wire carries a steady current upwards. Describe the magnetic field pattern around the wire as seen from above, including its direction, and state how the pattern changes when (i) the current is reversed and (ii) the current is doubled.

  • The field lines are concentric circles centred on the wire, with the lines further apart at greater distances because the field weakens. ✓
  • By the right-hand grip rule (thumb along the current, fingers curl with the field) the field is anticlockwise when viewed from above for a current flowing upwards. ✓
  • (i) Reversing the current reverses every arrow, so the field is clockwise; (ii) doubling the current doubles the flux density at every point, drawn as closer lines with the same circular shape. ✓
05
Calculation
[3 marks]

The horizontal component of the Earth's field at a location is 18 μT towards the north. A bar magnet is placed so that, at point X, its field is 18 μT towards the south, and at point Y its field is 54 μT towards the south. State what is special about X, and calculate the resultant field at Y and the direction a compass points there.

  • At X the two fields are equal and opposite, so the resultant is zero: X is a neutral point, where a compass has no preferred direction. ✓
  • At Y the fields are along the same line, so the resultant is 54 − 18 = 36 μT. ✓
  • The magnet's field dominates, so the resultant is 36 μT towards the south and the compass points south, reversed from its normal direction. ✓
06
Analysis
[4 marks]

A long solenoid carries a steady current. Viewed from its end A, the current is seen to flow clockwise round the turns.

(a) State the polarity of end A and describe the field pattern outside the solenoid. (b) Describe the field inside the solenoid, away from the ends, and how it is represented by field lines. (c) In a scale sketch of the field, the lines inside the solenoid are 2.0 mm apart where the flux density is 3.0 mT. Near one end the lines spread to 4.0 mm apart; estimate the flux density there.

  • (a) A clockwise current seen from end A makes A a south pole (anticlockwise would make it a north pole). ✓
  • Outside, the field is like that of a bar magnet: lines leave the north end, loop round and enter the south end A. ✓
  • (b) Inside, the field is strong and almost uniform, drawn as straight, parallel, equally spaced lines running along the axis from the south end to the north end. ✓
  • (c) Doubling the spacing halves the line density, so B = 3.0 × (2.0 / 4.0) = 1.5 mT. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.