Question
An α-particle and a proton are at rest a distance 20 μm apart in a vacuum, as illustrated in Fig. 4.1.
(a) (i) State Coulomb’s law.
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(ii) The α-particle and the proton may be considered to be point charges.
Calculate the electric force between the α-particle and the proton.
force = ……………………………………… N [2]
(b) (i) Define electric field strength.
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(ii) A point P is distance x from the α-particle along the line joining the α-particle to the proton (see Fig. 4.1). The variation with distance x of the electric field strength \(E_α\) due to the α-particle alone is shown in Fig. 4.2.
The variation with distance x of the electric field strength \(E_P\) due to the proton alone is also shown in Fig. 4.2.
1. Explain why the two separate electric fields have opposite signs.
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2. On Fig. 4.2, sketch the variation with x of the combined electric field due to the α-particle and the proton for values of x from 4 μm to 16 μm. [3]
Answer/Explanation
Ans:
(a) (i) force proportional to product of (two) charges and inversely proportional to square of separation reference to point charges
(ii) \(F = 2 × (1.6 × 10^{–19}) 2/ {4π × 8.85 × 10^{–12} × (20 × 10^{–6})^2}\)
\(F = 1.15 × 10^{–18}\) N
(b) (i) force per unit charge
on either a stationary charge
or a positive charge
(ii) 1. electric field is a vector quantity
electric fields are in opposite directions
charges repel
Any two of the above, 1 each
2. graph: line always between given lines
crosses x-axis between 11.0 μm and 12.3 μm
Question
An isolated solid metal sphere of radius r is given a positive charge. The distance from the centre of the sphere is x.
(a) The electric potential at the surface of the sphere is V0.
On the axes of Fig. 5.1, sketch a graph to show the variation with distance x of the electric potential due to the charged sphere, for values of x from x = 0 to x = 4r.
(b)The electric field strength at the surface of the sphere is E0.
On the axes of Fig. 5.2, sketch a graph to show the variation with distance x of the electric field strength due to the charged sphere, for values of x from x = 0 to x = 4r.
Answer/Explanation
(a)
graph: straight line at constant potential = V0 from x = 0 to x = r
curve with decreasing gradient
passing through (2r, 0.50V0) and (4r, 0.25V0)
(b)
graph: straight line at E = 0 from x = 0 to x = r
curve with decreasing gradient from (r, E0)
passing through (2r, ¼E0)