Electric Force Between Point Charges (Cambridge (CIE) A Level Physics)

Two point charges A and B are placed 0.014 mm apart as shown in Fig. 1.1. 

Fig. 1.1

The charge of A is +3.1 nC and the charge of B is −6.2 nC. The charges have the following radii: 

 r_A = 3.2 pm

 r_B = 4.1 pm

Determine the magnitude of the force between the two charges.

The magnitude of the electric forces between the charges is very high.

State and explain why this is the case.

(i) Draw arrows on Fig. 1.1 to show the direction of the electrostatic force coming from charges A and B.

[2]

(ii) Particle B is replaced by particle C. Particle C has a charge of +6.2 nC.   

Describe how the electrostatic force between charges A and C will be different to that between A and B. 

[2]

(iii) A positron is placed at point Y, equidistant from both A and B, as shown in Fig. 1.2. Fig. 1.2  

On Fig. 1.2 draw an arrow representing the direction of the resultant force acting on the positron.

[1]

An alpha particle and an aluminium nucleus are isolated in a vacuum, as shown in Fig. 1.1.

Each nucleus may be considered to be a point mass with a point charge.

Fig. 1.1

On Fig. 1.1, draw arrows to show the direction of the electric forces acting on the nuclei.

State one similarity and one difference between the gravitational force field and the electric force field around the nuclei.

An aluminium nucleus contains 13 protons.

The alpha particle and the aluminium nucleus are separated by a distance of 2.0 nm.

Calculate the electric force between the alpha particle and the aluminium nucleus.

The aluminium nucleus contains 27 nucleons in total.

(i) Calculate the gravitational force between the two nuclei. 

[2]

(ii) Suggest why gravitational effects do not need to be accounted for in electric field calculations involving nuclei.

[1]

Helium-3 is a light, stable isotope of helium with two protons and one neutron. 

The protons are assumed to be 1.88 × 10^–15 m apart.

For the two protons, calculate:

(i) the electrostatic force,

[2]

(ii) the gravitational force.

[2]

The force that holds the protons together in the nucleus is known as the strong nuclear force.

Suggest how your answers in (a) give evidence for the existence of the strong nuclear force.

State why the radius of the protons is not taken into account when calculating the electrostatic force between them.

The electrostatic force between an electron in the ground state of the helium-3 atom and the protons is 92 nN.

Show that the distance between the electron and the protons in the nucleus is about 50 pm.

Three fixed isolated point charges, ,   and are located as shown in Fig. 1.1 below. 

FIg. 1.1

has a charge of –30 µC,  has a charge of 50 µC and has a charge of 70 µC. is equidistant from charges  and . The right is taken as the positive x direction. 

Calculate the magnitude of the electric force on  from: 

(i)

[2]

(ii)           

[1]

Calculate the direction of the electric force with respect to the positive x-axis on Fig 1.1 from :

(i)

[2]

(ii)

[1]

Calculate the magnitude of the resultant force on .

Calculate the direction of the resultant force on  with respect to the x axis.

Two charged objects X and Y are made to circle a point O. X and Y are at a distance, d = 1.8 × 10⁻⁸ m and they have equal masses, where m = 1.7 × 10⁻⁹ kg as shown in Fig. 1.1.

The objects carry an equal but opposite charge, where the magnitude q = 3.2 × 10⁻¹⁹ C.

Fig. 1.1

Calculate the acceleration of X and Y.

Calculate the time required for the particles in part a) to make one complete orbit. 

A torque is experienced by particles X and Y from part a) when placed in an electric field of strength 6.5 V m⁻¹. The electric field acts perpendicular to the line between X and Y. 

Calculate the magnitude and explain the presence of the instantaneous torque when the particles are just starting to move in the electric field.

The particles X and Y in part a) are replaced with a gold nucleus of radius 7.0 fm, and an alpha particle of radius 1.7 fm. They are circling point O with the same separation d and are no longer in an electric field. 

Show that the separation of the gold nucleus and the alpha particle is around 90 x 10⁻¹⁶ larger than the separation of particles X and Y.