10.1 Describing Fields

A space shuttle of mass 2 × 10⁶ kg is travelling from the Earth to the moon. It accelerates uniformly from launch at 5.25 m s^–2.It has enough propellant to provide thrust for the first 124 seconds.

The mass of the Earth is 5.97 × 10²⁴ kg and the mean radius is 6.37 × 10⁶ m.

The Moon has a radius approximately 27% that of the Earth, and a mass of 1.2% that of the Earth. 

The gravitational field strength lines between the Earth and the moon can be drawn on a diagram.

Point P is the neutral point between the Earth and the moon where there is no resultant gravitational field.

Imagine that it was possible to construct a tunnel through the centre of the earth, connecting a point on the surface to the diametrically opposite point. Assume that the earth is perfectly spherical with an evenly distributed mass and that the mass and volume of the tunnel, air resistance and friction are negligible.

Within a hollow sphere of uniform density, the gravitational field strength is zero. 

• The distance from the centre of the earth = r
• The radius of the earth = R_e
• The gravitational field strength on the surface of the earth = g_surf

[3]

This case is analogous to a mass bouncing on a spring where , and where in this situation .

The time period for a mass on a spring, T, is equal to . For a satellite in orbit at a distance r, from the centre of a large body with mass M, the orbital speed can be obtained as .

Three charges are fixed at the corners of a right-angled triangle.

The length of both the horizontal and vertical sides is d.

Show that the electric potential at point P, halfway between the −2Q and −6Q charge is given by .

Before the discovery of quarks, scientists speculated that the subatomic particles might be made up of smaller particles.  
If an electron was made up of three smaller, identical particles with charge q, which are brought in from an infinite distance to the vertices of an equilateral triangle, it would have this arrangement.

The radius of an electron is 2.82 fm. 

In an electron gun, electrons are released from a cathode and accelerated towards an anode. The electrons leave the electron gun at 10% of the speed of light. 

A science fiction film director is planning for a battle scene between two spacecrafts. The first spacecraft uses an electron gun to fire a beam of electrons at the second spacecraft from close range. The electron beam is created by accelerating electrons from rest between electrodes with a potential difference of 120 V.  

To shield against the attack, the second aircraft creates a uniform electric field around itself and the electrons are stopped after 85 m. The director wishes to calculate the strength of the electric field, but is not aware of the equation .

After the failure of the first spacecraft to break through the electric shield of the second spacecraft a new weapon is to be designed. Instead of firing electrons, research is carried out to see if firing negatively charged ions with a charge of –2e and a mass of 2.26 × 10^-26 kg would be more effective. The second spacecraft uses the same electric field as in part (a) to shield itself and that the electric field is uniform.

Another option to attack the second spacecraft is to create a superweapon which can be fired from the aliens' home planet. As this weapon will fired from such a long way away from the second spacecraft, the spaceship and shield can be modelled as a charged particle carrying a charge of −130 C. The electrons fired by the superweapon have a kinetic energy of 12 MeV.