Fields and their Consequences
Fields and their consequences is the A-level Physics topic covering gravitational fields, electric fields and capacitors, treated as parallel force-at-a-distance topics. It uses field strength, potential and Newton's or Coulomb's law to analyse orbits, point charges, charged particles moving in fields and capacitor discharge.
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Method
- Use Newton's law of gravitation, F = G x M x m / r^2, and Coulomb's law, F = Q1 x Q2 / (4 x pi x epsilon0 x r^2), noting both are inverse-square laws for point masses or point charges.
- Calculate field strength as force per unit mass (g = G x M/r^2) or force per unit charge (E = k x Q/r^2) for a radial field, or E = V/d for a uniform field between parallel plates.
- Use potential (V = -G x M/r for gravity, V = k x Q/r for a point charge) to calculate the work done moving a mass or charge between two points, remembering gravitational potential is always negative.
- For satellites and orbits, equate the gravitational force to the centripetal force (G x M x m / r^2 = m x v^2/r) to derive relationships between orbital radius, speed and period.
- For capacitors, use Q = C x V and W = (1/2) x C x V^2, and combine capacitances in series (1/C = 1/C1 + 1/C2) or parallel (C = C1 + C2) as appropriate.
- For exponential capacitor discharge, use V = V0 x exp(-t / (R x C)), and take natural logs (ln V = ln V0 - t/(R x C)) to find R x C from the gradient of a straight-line graph.
Worked example
Two point charges are fixed 0.20 m apart in air: charge A = +4.0 x 10^-9 C and charge B = +6.0 x 10^-9 C. Calculate the electrostatic force between them, and state whether it is attractive or repulsive. (k = 1/(4 x pi x epsilon0) = 8.99 x 10^9 N m^2 C^-2)
- Identify the known values: Q1 = 4.0 x 10^-9 C, Q2 = 6.0 x 10^-9 C, r = 0.20 m, k = 8.99 x 10^9 N m^2 C^-2.
- Write down Coulomb's law: F = k x Q1 x Q2 / r^2.
- Substitute the values: F = (8.99 x 10^9 x 4.0 x 10^-9 x 6.0 x 10^-9) / (0.20)^2.
- Evaluate the numerator: 8.99 x 10^9 x 4.0 x 10^-9 x 6.0 x 10^-9 = 2.16 x 10^-7.
- Divide by r^2 = 0.040: F = 2.16 x 10^-7 / 0.040.
- Final answer: F = 5.4 x 10^-6 N, repulsive (since both charges are positive).
Practice questions
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Q1State Newton's law of gravitation in words.Show answer
Answer: The gravitational force between two point masses is proportional to the product of their masses and inversely proportional to the square of their separation.
Q2Calculate the gravitational field strength at the surface of a planet of mass 5.0 x 10^24 kg and radius 6.0 x 10^6 m. (G = 6.67 x 10^-11 N m^2 kg^-2)Show answer
Answer: 9.3 N/kg (g = GM/r^2 = (6.67 x 10^-11 x 5.0 x 10^24)/(6.0 x 10^6)^2)
Q3A capacitor of capacitance 220 uF is charged to a potential difference of 12 V. Calculate the charge stored.Show answer
Answer: 2.64 x 10^-3 C (Q = C x V = 220 x 10^-6 x 12)
Q4State what is meant by the electric potential at a point in an electric field.Show answer
Answer: The work done per unit positive charge in bringing a small test charge from infinity to that point.
Q5Two capacitors of 100 uF and 300 uF are connected in series. Calculate the combined capacitance.Show answer
Answer: 75 uF (1/C = 1/100 + 1/300 = 4/300, so C = 300/4)
Q6A satellite orbits a planet at radius r with orbital period T. Starting from equating gravitational force to centripetal force, show that T^2 is proportional to r^3.Show answer
Answer: T^2 = (4 x pi^2 / (G x M)) x r^3 (from G x M x m/r^2 = m x (4 x pi^2/T^2) x r, cancel m, then rearrange for T^2)
Exam-style questions
Written in the style of a A Level Science exam paper, with a full mark scheme.
State two similarities between gravitational fields and electric fields.
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A parallel plate capacitor has plates separated by 0.015 m with a potential difference of 300 V across them. Calculate the electric field strength between the plates, and the force on a charge of 2.0 x 10^-9 C placed between them.
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A 330 uF capacitor is charged to 8.0 V then discharged through a 20 kOhm resistor. Using V = V0 x exp(-t/(R x C)), calculate the potential difference across the capacitor 10.0 s after discharge begins.
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Free printable worksheet
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