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Fields · Question 10

Fields · Original GioPhysics question with a detailed, mark-by-mark answer guide.

Demand
discriminating
Marks
12
Topics
1
Answer
Complete
A rectangular coil rotating in a uniform magnetic fieldNSuniform field, B = 85 mTcoil of 250 turnsarea 3.2 × 10⁻³ m²axis of rotation50 revolutions per secondoutput to external circuit
Figure 6A rectangular coil hangs between the flat faces of two poles, the north pole a block on the left and the south pole a block on the right. Four evenly spaced horizontal arrows run across the gap from the north pole to the south pole, and a note reads 'uniform field, B = 85 mT'. The coil is drawn obliquely, as a rectangle turned so that its plane lies at an angle to the field, and is labelled 'coil of 250 turns' and 'area 3.2 × 10⁻³ m²'. A vertical dashed line through the middle of the coil is labelled 'axis of rotation', with a curved arrow above it and the note '50 revolutions per second'. Two leads run down from the bottom of the coil to a pair of slip rings with brushes, whose terminals are labelled 'output to external circuit'.
structured12 marks

A flat rectangular coil of 250 turns and area 3.2 × 10⁻³ m² is rotated at a constant rate in a uniform magnetic field of magnitude 85 mT. The axis of rotation is perpendicular to the field. The coil completes 50 revolutions per second.

  1. (a)

    State State Faraday's law of electromagnetic induction.

    2 marks
  2. (b)

    Determine Determine the maximum e.m.f. induced in the coil.

    3 marks
  3. (c)

    Explain Explain why the induced e.m.f. is zero at the instant when the plane of the coil is perpendicular to the magnetic field, even though the flux through the coil is greatest at that moment.

    3 marks
  4. (d)

    Discuss The output of the coil is connected to a resistor. Discuss the energy transfers taking place, and explain why more mechanical power must be supplied to keep the coil rotating at 50 revolutions per second once the resistor is connected.

    4 marks
Ready to self-mark?Reveal the detailed answer guide
Answer overviewKey answer: the magnitude of the induced e.m.f. is equal to the rate of change of magnetic flux linkage expressed as ε = −N dΦ/dt, the minus sign expressing Lenz's law ω = 2πf = 2π × 50 = 314 rad s⁻¹
01

(a)

2 marks

State State Faraday's law of electromagnetic induction.

How to approach it

Answer the command word directly and use precise physical vocabulary. Include only the distinct features or facts that earn marks, without burying them in unrelated background information.

  1. 1

    the magnitude of the induced e.m.f. is equal to the rate of change of magnetic flux linkage

  2. 2

    expressed as ε = −N dΦ/dt, the minus sign expressing Lenz's law

02

(b)

3 marks

Determine Determine the maximum e.m.f. induced in the coil.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    ω = 2πf = 2π × 50 = 314 rad s⁻¹

  2. 2

    ε₀ = NBAω = 250 × 0.085 × 3.2 × 10⁻³ × 314

  3. 3

    ε₀ = 21 V

03

(c)

3 marks

Explain Explain why the induced e.m.f. is zero at the instant when the plane of the coil is perpendicular to the magnetic field, even though the flux through the coil is greatest at that moment.

How to approach it

State the outcome first, then link cause to effect with the relevant physical principle. Each link in the reasoning should be explicit enough to earn its own marking point.

  1. 1

    the induced e.m.f. depends on the rate of change of flux, not on the flux itself

  2. 2

    when the plane of the coil is perpendicular to the field the flux is at a maximum, and at a maximum its rate of change is momentarily zero

  3. 3

    so the e.m.f. is zero there and greatest a quarter of a cycle later, when the flux is passing through zero and changing fastest

04

(d)

4 marks

Discuss The output of the coil is connected to a resistor. Discuss the energy transfers taking place, and explain why more mechanical power must be supplied to keep the coil rotating at 50 revolutions per second once the resistor is connected.

How to approach it

Build a chain of claim, evidence and physics reasoning. Address more than one relevant factor, identify a limitation or assumption, and finish with a conclusion that is conditional on the evidence rather than absolute.

  1. 1

    with the circuit closed, the induced e.m.f. drives a current through the coil and the resistor, and electrical energy is dissipated in the resistor as thermal energy

  2. 2

    the current-carrying coil sits in the magnetic field, so it experiences a torque

  3. 3

    by Lenz's law that torque opposes the rotation of the coil

  4. 4

    so an external agent must do work against it, and the mechanical power supplied equals the electrical power dissipated — energy is conserved, with the coil acting as the converter rather than the source

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