18. Electric fields
A section of Physics, 9702
Listing 10 of 195 questions
Two solid metal spheres A and B, each of radius 1.5 cm, are situated in a vacuum. Their centres are separated by a distance of 20.0 cm, as shown in . P sphere A sphere B x 20.0 cm 1.5 cm 1.5 cm (not to scale) Both spheres are positively charged. Point P lies on the line joining the centres of the two spheres, at a distance x from the centre of sphere A. The variation with distance x of the electric field strength E at point P is shown in . –10 –20 –30 –40 –50 x / cm E / N C–1 Use to determine the ratio magnitude of charge on sphere A magnitude of charge on sphere B . Explain your working. ratio = The variation with distance x of the electric potential V at point P is shown in . 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 V / V x / cm An α-particle is initially at rest on the surface of sphere A. The α-particle moves along the line joining the centres of the two spheres. Determine, for the α-particle as it moves between the two spheres, its maximum speed, maximum speed = m s–1 its speed on reaching the surface of sphere B. speed = m s–1
9702_w16_qp_42
THEORY
2016
Paper 4, Variant 2
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Two small solid metal spheres A and B have equal radii and are in a vacuum. Their centres are 15 cm apart. Sphere A has charge +3.0 pC and sphere B has charge +12 pC. The arrangement is illustrated in . 15 cm 5.0 cm P sphere A charge + 3.0 pC sphere B charge + 12 pC Point P lies on the line joining the centres of the spheres and is a distance of 5.0 cm from the centre of sphere A. Suggest why the electric field strength in both spheres is zero. Show that the electric field strength is zero at point P. Explain your working. Calculate the electric potential at point P. electric potential = V A silver-107 nucleus (107 47 Ag) has speed v when it is a long distance from point P. Use your answer in to calculate the minimum value of speed v such that the nucleus can reach point P. speed = m s−1
9702_w16_qp_43
THEORY
2016
Paper 4, Variant 3
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State Coulomb’s law for the force between two point charges. Two point charges are situated in a vacuum and separated by a distance R. The force between the charges is FC. On , sketch a graph to show the variation of the force F between the charges with separation x for values of x from x = R to x = 4R. R 0.2 Fc 0.4 Fc 0.6 Fc F 0.8 Fc 1.0 Fc 2R 3R 4R x Two coils C and D are placed close to one another, as shown in . I coil C coil D V e.m.f. E
9702_w17_qp_41
THEORY
2017
Paper 4, Variant 1
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State Coulomb’s law for the force between two point charges. Two point charges are situated in a vacuum and separated by a distance R. The force between the charges is FC. On , sketch a graph to show the variation of the force F between the charges with separation x for values of x from x = R to x = 4R. R 0.2 Fc 0.4 Fc 0.6 Fc F 0.8 Fc 1.0 Fc 2R 3R 4R x Two coils C and D are placed close to one another, as shown in . I coil C coil D V e.m.f. E
9702_w17_qp_43
THEORY
2017
Paper 4, Variant 3
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State what is meant by the electric potential at a point, the relationship between electric potential at a point and electric field strength at the point. Two similar solid metal spheres A and B, each of radius R, are situated in a vacuum such that the separation of their centres is D, as shown in . R R sphere A charge +Q D P x sphere B charge +q The charge +Q on sphere A is larger than the charge +q on sphere B. A movable point P is located on the line joining the centres of the two spheres. The point P is a distance x from the centre of sphere A.
9702_w18_qp_42
THEORY
2018
Paper 4, Variant 2
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Define electric potential. An isolated conducting sphere in a vacuum has radius r and is initially uncharged. It is then charged by friction so that it carries a final charge Q. This charge can be considered to be acting at the centre of the sphere. By considering the electric potential at its surface, show that the capacitance C of the sphere is given by C = 4πε0r where ε0 is the permittivity of free space. The dome of an electrostatic generator is a spherical conductor of radius 13 cm. It is initially charged so that the electric potential at the surface is 4.5 kV. A smaller isolated sphere of radius 5.2 cm, initially uncharged, is brought near to the dome. Sparking causes a current between the two spheres until they reach the same potential. Assume that any charge on a sphere may be considered to act as a point charge at its centre. Calculate the charge that is transferred between the two spheres. charge = C
9702_w21_qp_42
THEORY
2021
Paper 4, Variant 2
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Define electric potential at a point. An isolated conducting sphere is charged. shows the variation of the potential V due to the sphere with displacement x from its centre. – 1000 – 750 – 500 – 250 – 0.1 0.1 0.2 0.3 – 0.2 – 0.3 V / V x / m Use to determine: the radius of the sphere radius = m the charge on the sphere. charge = C Two spheres are identical to the sphere in . Each sphere has the same charge as the sphere in . The spheres are held in a vacuum so that their centres are separated by a distance of 0.46 m. Assume that the charge on each sphere is a point charge at the centre of the sphere. Calculate the electric potential energy EP of the two spheres. EP = J The two spheres are now released simultaneously so that they are free to move. Describe and explain the subsequent motion of the spheres.
9702_w22_qp_42
THEORY
2022
Paper 4, Variant 2
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State the relationship between electric field and electric potential. Two charged isolated insulating spheres X and Y are near to each other, as shown in . X Y P P is a point on the line joining the centres of the spheres. Explain why it is not possible for the total electric potential and the resultant electric field to simultaneously be zero at point P. The magnitudes of the charges on spheres X and Y in are Q and 2Q respectively. The spheres may be considered as point charges at their centres. Point P is a distance x from the centre of sphere X. The electric potential at point P is zero. Show that the distance y of point P from the centre of sphere Y is equal to 2x. State an expression, in terms of Q, x and the permittivity of free space ε0, for the electric field strength EX at P due to sphere X. EX = Determine an expression, in terms of Q, x and ε0, for the resultant electric field strength E at point P due to the two spheres. E =
9702_w24_qp_41
THEORY
2024
Paper 4, Variant 1
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State the relationship between electric field and electric potential. Two charged isolated insulating spheres X and Y are near to each other, as shown in . X Y P P is a point on the line joining the centres of the spheres. Explain why it is not possible for the total electric potential and the resultant electric field to simultaneously be zero at point P. The magnitudes of the charges on spheres X and Y in are Q and 2Q respectively. The spheres may be considered as point charges at their centres. Point P is a distance x from the centre of sphere X. The electric potential at point P is zero. Show that the distance y of point P from the centre of sphere Y is equal to 2x. State an expression, in terms of Q, x and the permittivity of free space ε0, for the electric field strength EX at P due to sphere X. EX = Determine an expression, in terms of Q, x and ε0, for the resultant electric field strength E at point P due to the two spheres. E =
9702_w24_qp_43
THEORY
2024
Paper 4, Variant 3
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Define electric potential at a point. Two isolated point charges A and B are separated by a distance of 30.0 cm, as shown in . x 30.0cm A B The charge at A is + 3.6 × 10–9 C. The variation with distance x from A along AB of the potential V is shown in . –200 –400 –600 V / V x / cm State the value of x at which the potential is zero. x = cm Use your answer in to determine the charge at B. charge = C A small test charge is now moved along the line AB in from x = 5.0 cm to x = 27 cm. State and explain the value of x at which the force on the test charge will be maximum.
9702_s08_qp_4
THEORY
2008
Paper 4, Variant 0
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Questions Discovered
195