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A Level · A2 · structured

A Level extension · Question 10

A Level extension · Original GioPhysics question with a detailed, mark-by-mark answer guide.

Demand
demanding
Marks
11
Topics
3
Answer
Complete
Two parallel metal plates in a vacuum, connected to a 2.0 kV supply2.0 kV+−vacuum5.0 mm
Fig. 10.1Two long horizontal metal plates are drawn one directly above the other and connected by wires at their left-hand ends to a battery labelled 2.0 kV; the upper plate carries a plus sign and the lower plate a minus sign. The space between the plates is empty and labelled vacuum, and a dimension at the right-hand end gives the separation of the plates as 5.0 mm. No field lines are drawn between the plates.
structured11 marks

Two large parallel metal plates are 5.0 mm apart in a vacuum. A potential difference of 2.0 kV is maintained between them. A separate circuit contains a capacitor of capacitance 22 μF charged to a potential difference of 12 V.

  1. (a)

    Calculate Calculate the magnitude of the electric field strength between the parallel plates.

    2 marks
  2. (b)

    Explain Compare the field between the parallel plates with the field around an isolated point charge, and explain the difference in how each varies with position.

    3 marks
  3. (c)

    Calculate Calculate the energy stored in the 22 μF capacitor.

    2 marks
  4. (d)

    Determine The charged capacitor is discharged through a 150 kΩ resistor. Determine the time taken for the potential difference across it to fall to 3.0 V.

    4 marks
Ready to self-mark?Reveal the detailed answer guide
Answer overviewKey answer: E = V/d = 2000 / 5.0 × 10⁻³ E = 4.0 × 10⁵ V m⁻¹ the field between the plates is uniform — the field lines are parallel and equally spaced, so E has the same magnitude and direction everywhere between them
01

(a)

2 marks

Calculate Calculate the magnitude of the electric field strength between the parallel plates.

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

    E = V/d = 2000 / 5.0 × 10⁻³

  2. 2

    E = 4.0 × 10⁵ V m⁻¹

02

(b)

3 marks

Explain Compare the field between the parallel plates with the field around an isolated point charge, and explain the difference in how each varies with position.

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 field between the plates is uniform — the field lines are parallel and equally spaced, so E has the same magnitude and direction everywhere between them

  2. 2

    the field of a point charge is radial, with lines spreading out from the charge

  3. 3

    so the point-charge field falls off as 1/r², while the field between the plates does not vary with position at all

03

(c)

2 marks

Calculate Calculate the energy stored in the 22 μF capacitor.

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

    W = ½CV² = ½ × 22 × 10⁻⁶ × 12²

  2. 2

    W = 1.6 × 10⁻³ J

04

(d)

4 marks

Determine The charged capacitor is discharged through a 150 kΩ resistor. Determine the time taken for the potential difference across it to fall to 3.0 V.

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

    time constant RC = 150 × 10³ × 22 × 10⁻⁶ = 3.3 s

  2. 2

    V = V₀e^(−t/RC), so 3.0 = 12e^(−t/3.3)

  3. 3

    t = RC ln(V₀/V) = 3.3 × ln 4

  4. 4

    t = 4.6 s

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