Coursework 13: Electric and Gravitational Forces and Fields

Gravitational constant G = 6.67 × 10^-11 N m² kg^-2

Permittivity of free space ε₀ = 8.85 × 10^-12 C² N^-1 m²

Charge on an electron e = -1.60 × 10^-19 C

Mass of an electron m_e = 9.11 × 10^-31 kg

Mass of a proton m_P = 1.67 × 10^-27 kg

Mass of the Sun M_S = 1.99 × 10³⁰ kg

Radius of the Earth R_E = 6.37 × 10⁶ m

Mass of Earth M_E = 5.98 × 10²⁴ kg

Earth to Sun distance R_ES = 150 × 10⁹ m

Note: Any constants you need from this list for Exams will be given to you

1) Two +10.0 nC point charges are 2.00 cm apart on the x-axis.

a) What is the net force on a +1.00 nC point charge placed midway between them?

b) What is the net force on the middle charge if the charge on the right is replaced

by a -10.0 nC charge? (4 marks)

2) What is the Sun’s gravitational field at the position of the Earth? Use your answer to determine the force of the Earth on the Sun. (4 marks)

3) Consider a small particle of mass 1.00 gram near the surface of the Earth. If the particle carries a charge of -3.00 nC what are the magnitude and direction of the electric field that provides a force which exactly balances the weight of the particle? (4 marks)

4) With reference to the diagram below, obtain the magnitude and direction of the electric field at the -10.0 nC charge due to the other two charges. What is the force acting on the -10.0 nC charge? (6 marks)

5) a) Calculate the electric field intensity and the electric potential at a point midway

between two point charges of +10^-9 C and -10^-9 C which are 20.0 cm apart in a vacuum.

b) An electric field intensity of the same magnitude as in part a) exists between two

large area parallel conducting plates. If the plates are situated 2.00 cm apart in air,

what is the potential difference between them? (6 marks)

6) a) Find the gravitational field at the orbit of the space shuttle which is 300,000 m above

the Earth’s surface. Hence obtain the force due to gravity on an astronaut of mass 75.0 kg in the orbiting space shuttle. Why does an astronaut in the orbiting shuttle appear weightless?

b) Determine the speed of the shuttle when in this orbit. (6 marks)

7) A projectile of mass 1000 kg is launched vertically upwards from Earth.

a) What is the gravitational potential due to the Earth at a height of 400 km?

b) What is its gravitational potential energy of the projectile at a height of 400 km?

c) What was the initial speed of the projectile at launch if its speed at 400 km is 500 s^-1?

(Assume that after launch no other forces apart from gravity act on the projectile). (6 marks)

8) A beam of electrons is directed at a target. They are accelerated from rest through 12.0 cm in a uniform electric field of magnitude 7.50 × 10⁵ NC^-1.

a) Find the potential difference through which the electrons have been accelerated.

b) Calculate the final kinetic energy in eV of one of these electrons. (4 marks)

9) An electron travels at a speed of 2.00 × 10⁵ m s^-1 through a point A and continues to another point B. If the potential at B is higher than that at A by 100 V, what is the speed of the electron as it passes through point B?

(4 marks)

10) A parallel plate capacitor consists of two plates each of area 3.00 × 10^-4 m² separated by 2.00 mm. It is charged so that the potential difference is 500 V.

a)What is the force on a proton placed between the plates at a distance of 0.500 mm from the negative plate.

b) A proton is projected at a speed of 2.00 × 10⁵ m s^-1 through a small hole in the negative plate and travels directly towards the positive plate. Will it reach the positive plate? If not, how far will it travel before falling back to the negative plate?

(6 marks)

11) An isolated metal sphere of radius 2.00 cm carries a negative charge of 2.00 × 10^-8 C.

a) Calculate the potential at the surface of the sphere.

b) How much work is done in moving a positive charge of 1.60 × 10^-6 C from the sphere’s surface to a point 3.00 cm above the surface?

c) What are the electric field E and the electric potential inside the metal sphere at a radial distance of 1.00 cm from the centre of the sphere?

(6 marks)

12) Using clear, precise English and mathematical expressions:

a) Define the electric potential field.

b) Derive an expression for the potential at a distance r from a point charge Q.

c) Explain why the potential inside a charged conductor has a non-zero constant value. (6 marks)

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