7.4 Electric Fields

Figure 1 below shows a diagram of ions in a mass spectrometer. 

Figure 1

The magnetic field strength in the velocity selector is 0.18 T. 

Calculate the separation of the plates, din the velocity selector needed to select a velocity of 120 km s^–1.

The velocity selector plates are now isolated from the mass spectrometer so only an electric field is between the plates and the potential difference remains the same as before. 

A beam of protons enter between the plates at right angles to the electric field. The horizontal velocity of the protons is 500 km s^–1. The path of the protons is shown in Figure 2. 

Figure 2

The horizontal length of each plate is 70 mm. X is a point midway between the plates.

Show that the vertical velocity of a proton at point X is about 140 km s^–1.

Calculate the magnitude of the resultant velocity of a proton at X.

Three fixed isolated point charges, ,   and  are located as shown in Figure 1 below. 

Figure 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: 

          

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

Calculate the magnitude of the resultant force on .

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

An electric dipole shown in Figure 1 consists of two separated point charges of the opposite charge. 

A pair of charges +6 nC and –6 nC are separated by a distance d of 3.15 × 10^–14 m to make an electric dipole and is placed in a uniform electric field. 

Figure 1

Describe what happens to the dipole in the field.

The electric field strength of the uniform electric field is 5.1 N. 

Calculate the moment of the electric dipole.

The dipole is reset to its original horizontal position, and the same electric field is now placed at an angle of 30º to the horizontal plane of the dipole as shown in Figure 2. 

Figure 2

Show that the moment of the electric dipole is now halved.

Figure 1 shows a simple pendulum with a length of 8 cm and a bob of mass 2.0 × 10^–19 kg and charge q of +2e. The pendulum is suspended between two vertical plates with a uniform electric field of 3.0 N C^–1. The bob is slightly displaced from its equilibrium and begins to oscillate.

 Figure 1

The time period, T of a pendulum is given by the equation: 

      T = 

Where l is the length of the string and  is the net acceleration acting on the charged particle. 

Calculate the time period of the oscillation of the pendulum.

The pendulum is removed from the electric field. It is now displaced by an insulated rod with a charged sphere X positioned close to it,where it then remains in equilibrium. The string makes an angle with the vertical as shown in Figure 2. 

Figure 2

The charge on the sphere X is –4e and the separation between the centres of the two spheres is 3.1 cm. 

Calculate the angle  made by the string with the vertical.

Point A, of +6.0 nC, and B, of – 4.0 nC, are 500 mm apart in a vacuum, as shown in Figure 1. The point P is 300 mm from A and 400 mm from B. 

Figure 1

Calculate the component of the electric field at P in the direction PB.

Calculate the component of the electric field at P in the direction AP.

Hence, calculate the magnitude and direction of the resultant electric field at P.

The point P is now 600 mm from A and 800 mm from B. 

State and explain the effect this will have on the direction and magnitude of the resultant electric field at P.

Figure 1 shows an electron that enters an electric field at right angles to the field. 

Figure 1

Figure 2 shows a small polystyrene ball which is suspended between two vertical metal plates, P₁ and P₂, distance d apart that are initially uncharged.
The ball carries a charge of –0.13 μC. 

Figure 2

When the switch is closed, a p.d. of 400 V is applied between P₁ and P₂ and the ball experiences an electrostatic force of 28 mN. 

Calculate the value d.

Because of the electrostatic force acting on it, the ball is displaced from its original position. It comes to rest when the suspended thread makes an angle θ with the vertical, as shown in Figure 3. 

Figure 3

On Figure 2, mark and label the forces that act on the ball when it is in this position.

For the ball to be in equilibrium, the angle  is at 17 º. 

Calculate the mass of the ball.

An alpha particle was deflected while passing through thin gold foil. The alpha particle passed within 6.0 pm of a gold nucleus. 

Calculate the magnitude and direction of the electrostatic force experienced by the alpha particle. 

   Atomic number of gold = 79.

Figure 1 shows a negative ion which has a charge of –4e and is free to move in a uniform electric field. 

Figure 1

State the direction of the electrostatic force on the ion and explain its motion as it starts to move in this field.

The ion experiences an electrostatic force of 4.5 × 10^–15 N. 

Calculate the electric field strength of the uniform electric field.

The field lines are now reversed to the opposite direction. 

Describe what happens to the motion of the ion.

Figure 1 shows particle P with charge +2e halfway between two parallel metal plates separated by a distance of 65 mm. The plates are connected to a voltage supply of 20 V. 

Figure 1

Midway between the plates, particle P remains at rest. 

Calculate the mass of particle P.

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. 

The separation of A and B is halved without changing their charges or masses. 

State and explain the effect, if any, this will have on the resultant force between A and B.

At the original separation, the charge of A is doubled, whilst the mass of A and the charge of B remain as they were initially. 

State what would have to happen to the mass of B to keep the resultant force zero.