18.3. Electric force between point charges
A subsection of Physics, 9702, through 18. Electric fields
Listing 10 of 28 questions
Two positively charged identical metal spheres A and B have their centres separated by a distance of 24 cm, as shown in . sphere A x sphere B 24 cm (not to scale) The variation with distance x from the centre of A of the electric field strength E due to the two spheres, along the line joining their centres, is represented in . E / 104 N C–1 x / cm – 2 – 1 State the radius of the two spheres. radius = cm The charge on sphere A is 3.6 × 10−9 C. Determine the charge QB on sphere B. Assume that spheres A and B can be treated as point charges at their centres. Explain your working. QB = C Sphere B is removed. Use information from to determine the electric potential on the surface of sphere A. electric potential = V Calculate the capacitance of sphere A. capacitance = F
9702_m20_qp_42
THEORY
2020
Paper 4, Variant 2
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State Coulomb’s law. A charged sphere X is supported on an insulating stand. A second charged sphere Y is suspended by an insulating thread so that sphere Y is in equilibrium at the position shown in . 0.080 m sphere X charge +96 nC vertical line thread stand sphere Y charge +64 nC 1.2 m The charge on sphere X is +96 nC and the charge on sphere Y is +64 nC. Assume that the spheres behave as point charges. The length of the thread is 1.2 m and the centres of sphere X and sphere Y are separated horizontally by a distance of 0.080 m. On , draw and label all the forces acting on sphere Y. Determine the mass of sphere Y. mass = kg Calculate the total electric potential energy stored between X and Y. energy = J An electron enters the region between two parallel plates P and Q, that are separated by a distance of 18 mm, as shown in . 18 mm path of electron plate P +250 V plate Q The space between the plates is a vacuum. The potential difference between the plates is 250 V. The electric field may be assumed to be uniform in the region between the plates and zero outside this region. State the direction of the electric force on the electron when between the plates. Determine the magnitude of the force acting on the electron due to the electric field. force = N Explain why the electron does not follow a circular path.
9702_m23_qp_42
THEORY
2023
Paper 4, Variant 2
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Two point charges A and B each have a charge of + 6.4 × 10–19 C. They are separated in a vacuum by a distance of 12.0 μm, as shown in . 12.0 μm A P Q B 3.0 μm +6.4 × 10–19 C +6.4 × 10–19 C 3.0 μm Points P and Q are situated on the line AB. Point P is 3.0 μm from charge A and point Q is 3.0 μm from charge B. Calculate the force of repulsion between the charges A and B. force = N Explain why, without any calculation, when a small test charge is moved from point P to point Q, the net work done is zero. Calculate the work done by an electron in moving from the midpoint of line AB to point P. work done = J
9702_s10_qp_42
THEORY
2010
Paper 4, Variant 2
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Two point charges A and B each have a charge of + 6.4 × 10–19 C. They are separated in a vacuum by a distance of 12.0 μm, as shown in . 12.0 μm A P Q B 3.0 μm +6.4 × 10–19 C +6.4 × 10–19 C 3.0 μm Points P and Q are situated on the line AB. Point P is 3.0 μm from charge A and point Q is 3.0 μm from charge B. Calculate the force of repulsion between the charges A and B. force = N Explain why, without any calculation, when a small test charge is moved from point P to point Q, the net work done is zero. Calculate the work done by an electron in moving from the midpoint of line AB to point P. work done = J
9702_s10_qp_43
THEORY
2010
Paper 4, Variant 3
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Define electric field strength. An isolated metal sphere is to be used to store charge at high potential. The charge stored may be assumed to be a point charge at the centre of the sphere. The sphere has a radius of 25 cm. Electrical breakdown (a spark) occurs in the air surrounding the sphere when the electric field strength at the surface of the sphere exceeds 1.8 × 104 V cm–1. Show that the maximum charge that can be stored on the sphere is 12.5 μC. Calculate the potential of the sphere for this maximum charge. potential = V
9702_s12_qp_41
THEORY
2012
Paper 4, Variant 1
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Define electric field strength. An isolated metal sphere is to be used to store charge at high potential. The charge stored may be assumed to be a point charge at the centre of the sphere. The sphere has a radius of 25 cm. Electrical breakdown (a spark) occurs in the air surrounding the sphere when the electric field strength at the surface of the sphere exceeds 1.8 × 104 V cm–1. Show that the maximum charge that can be stored on the sphere is 12.5 μC. Calculate the potential of the sphere for this maximum charge. potential = V
9702_s12_qp_43
THEORY
2012
Paper 4, Variant 3
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A helium nucleus contains two protons. In a model of the helium nucleus, each proton is considered to be a charged point mass. The separation of these point masses is assumed to be 2.0 × 10−15 m. For the two protons in this model, calculate the electrostatic force, electrostatic force = N the gravitational force. gravitational force = N Using your answers in , suggest why there must be some other force between the protons in the nucleus, this additional force must have a short range.
9702_s14_qp_42
THEORY
2014
Paper 4, Variant 2
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By reference to electric field lines, explain why, for points outside an isolated spherical conductor, the charge on the sphere may be considered to act as a point charge at its centre. Two isolated protons are separated in a vacuum by a distance x. Calculate the ratio electric force between the two protons gravitational force between the two protons . ratio = By reference to your answer in , suggest why gravitational forces are not considered when calculating the force between charged particles.
9702_s16_qp_42
THEORY
2016
Paper 4, Variant 2
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State Coulomb’s law. Two charged metal spheres A and B are situated in a vacuum, as illustrated in . sphere B sphere A P x 6.0 cm The shortest distance between the surfaces of the spheres is 6.0 cm. A movable point P lies along the line joining the centres of the two spheres, a distance x from the surface of sphere A. The variation with distance x of the electric field strength E at point P is shown in . –5 –10 –15 x / cm E / 103 V m–1 Use to explain whether the two spheres have charges of the same, or opposite, sign. A proton is at point P where x = 5.0 cm. Use data from to determine the acceleration of the proton. acceleration = m s–2 Use data from to state the value of x at which the rate of change of electric potential is maximum. Give the reason for the value you have chosen.
9702_s17_qp_42
THEORY
2017
Paper 4, Variant 2
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Questions Discovered
28