Homework – Electric fields
Name:
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Class:
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Date:
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Time:
60 minutes
Marks:
50 marks
/50
%
Page 1 of 11
Q1.
(a)
(i)
Define electric field strength, and state whether it is a scalar quantity or a
vector quantity.
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(ii)
Complete the diagram below to show the electric field lines in the region
around two equal positive point charges. Mark with a letter N the position of
any point where the field strength is zero.
(6)
(b)
Point charges A, of +2.0 nC, and B, of –3.0 nC, are 200 mm apart in a vacuum, as
shown by the figure. The point P is 120 mm from A and 160 mm from B.
(i)
Calculate the component of the electric field at P in the direction AP.
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Page 2 of 11
(ii)
Calculate the component of the electric field at P in the direction PB.
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(iii)
Hence calculate the magnitude and direction of the resultant field at P.
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(6)
(c)
(i)
Explain why there is a point X on the line AB in part (b) at which the electric
potential is zero.
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(ii)
Calculate the distance of the point X from A.
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(4)
(Total 16 marks)
Page 3 of 11
Q2.
(a)
An electron moves parallel to, but in the opposite direction to, a uniform electric
field, as shown in Figure 1.
Figure 1
(i)
State the direction of the force acting on the electron due to the electric field.
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(ii)
What is the effect of this force on the motion of the electron?
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(2)
(b)
An electron, which is travelling in a horizontal path at constant speed, enters a
uniform vertical electric field as shown in Figure 2.
Figure 2
(i)
Sketch on Figure 2 the path followed by the electron.
(ii)
Explain the motion of the electron whilst in this field.
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(3)
(Total 5 marks)
Page 4 of 11
Q3.
Both gravitational and electric field strengths can be described by similar equations written
in the form
(a)
Complete the following table by writing down the names of the corresponding
quantities, together with their SI units, for the two types of field.
symbol
a
gravitational field
quantity
SI unit
electrical field
quantity
SI unit
gravitational
field strength
m F–1
b
c
d
(4)
(b)
Two isolated charged objects, A and B, are arranged so that the gravitational force
between them is equal and opposite to the electric force between them.
(i)
The separation of A and B is doubled without changing their charges or
masses. State and explain the effect, if any, that this will have on the resultant
force between them.
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(ii)
At the original separation, the mass of A is doubled, whilst the charge on A
and the mass of B remain as they were initially. What would have to happen to
the charge on B to keep the resultant force zero?
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(3)
(Total 7 marks)
Page 5 of 11
Q4.
The Earth has an electric charge. The electric field strength outside the Earth varies in the
same way as if this charge were concentrated at the centre of the Earth. The axes in the
diagram below represent the electric field strength E and the distance from the centre of
the Earth r. The electric field strength at A has been plotted.
(a)
(i)
Determine the electric field strength at B and then complete the graph to show
how the electric field strength varies with distance from the centre of the Earth
for distances greater than 6400 km.
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(3)
(ii)
State how you would use the graph to find the electric potential difference
between the points A and B.
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(1)
Page 6 of 11
(b)
The permittivity of free space ε0 is 8.9 × 10–12 F m–1 .
(i)
Calculate the total charge on the Earth.
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(2)
(ii)
The charge is distributed uniformly over the Earth's surface. Calculate the
charge per square metre on the Earth's surface.
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(2)
(Total 8 marks)
Page 7 of 11
Q5.
A small charged sphere of mass 2.1 × 10 –4 kg, suspended from a thread of insulating
material, was placed between two vertical parallel plates 60 mm apart. When a potential
difference of 4200 V was applied to the plates, the sphere moved until the thread made an
angle of 6.0° to the vertical, as shown in the diagram below.
(a)
Show that the electrostatic force F on the sphere is given by F = mg tan 6.0°
where m is the mass of the sphere.
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(3)
(b)
Calculate
(i)
the electric field strength between the plates,
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(ii)
the charge on the sphere.
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(3)
(Total 6 marks)
Page 8 of 11
Q6.
(a)
An electron travels at a speed of 3.2 × 10 7 ms–1 in a horizontal path through a
vacuum. The electron enters the uniform electric field between two parallel plates,
30 mm long and 15 mm apart, as shown in the figure below. A potential difference of
1400 V is maintained across the plates, with the top plate having positive polarity.
Assume that there is no electric field outside the shaded area.
(i)
Show that the electric field strength between the plates is 9.3 × 10 4 Vm–1.
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(ii)
Calculate the time taken by the electron to pass through the electric field.
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Page 9 of 11
(iii)
Show that the acceleration of the electron whilst in the field is 1.6 × 10 16 m s–2
and state the direction of this acceleration.
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(5)
(b)
Determine the magnitude and direction of the velocity of the electron at the point
where it leaves the field.
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(3)
(Total 8 marks)
Page 10 of 11
Page 11 of 11