Electric Fields

Define electric field strength.

The electric field is produced by applying a potential difference of $4.0\ \text{kV}$ between two charged parallel metal plates.

1. Calculate the separation between the plates.

separation = ______ $\text{m}$

1. Describe the arrangement of the two plates. Include in your answer a statement of the sign of the charge on each plate. You may draw on Fig. 4.1.

Determine the magnitude and direction of the force on sphere Y.

magnitude = ______ $\text{N}$
direction ______

The electric forces acting on the two spheres form a couple. This couple acts on the rod with a torque of $6.2 \times 10^{-16}\ \text{N m}$.

Calculate the angle $\theta$ of the rod to the horizontal.

$\theta$ = ______ $^{\circ}$

On Fig. 6.1, draw at least six field lines to represent the electric field between the plates.

An $\alpha$-particle travels in a vacuum between the two plates.

The electric field does work on the $\alpha$-particle. The gain in kinetic energy of the $\alpha$-particle is $15\ \text{keV}$.

Calculate the electric field strength between the plates.

electric field strength = ______ $\text{V m}^{-1}$

Explain what is meant by an electric field.

On Fig. 7.1, draw lines to represent the electric field between the plates.

Calculate the electric field strength between the plates.

electric field strength = ______ $\text{V m}^{-1}$

Calculate the work done by the electric field on the $\alpha$-particle as it moves from AB to CD.

work done = ______ $\text{J}$

A $\beta$-particle moves from AB to CD. Calculate the ratio

Show your working.

ratio = ______

On Fig. 7.1, draw six field lines to represent the electric field between the metal plates.

Calculate the electric field strength $E$ between the plates.

$E$ = ______ $\text{V m}^{-1}$

There is a force acting on A due to the electric field between the plates.
Show that this force is $4.8 \times 10^{-15}\text{ N}$.

The insulating rod joining A and B is fixed in the position shown in Fig. 7.2.
Calculate the torque of the couple acting on the rod.

torque = ______ unit ______

The insulating rod is now released so that it is free to rotate about C.
State and explain the position of the rod when it comes to rest.

Define electric field strength.

On Fig. 4.1, draw lines to represent the electric field between the plates.

Calculate the electric field strength between the plates.

electric field strength = ______ $\text{V m}^{-1}$

Calculate the charge on the drop.

charge = ______ $\text{C}$

The potential of the upper plate is increased. Describe and explain the subsequent motion of the drop.

The magnitude of $V$ is increased.

The separation $d$ of the plates is decreased.

charge

mass

speed

The electric field gives rise to an acceleration of the $\alpha$-particles and the $\beta$-particles. Determine the ratio

ratio = ______

State what is meant by an electric field.

On Fig. 5.1, label each sphere with (+) or (–) to show its charge.

On Fig. 5.1, mark a region where the magnitude of the electric field is

1. constant (label this region C),

2. decreasing (label this region D).

On Fig. 5.2, draw an arrow at P and an arrow at N to show the directions of the forces due to the applied electric field at each of these points.

Calculate the torque on the molecule produced by the forces in (i).

torque = ______ $\text{N m}$

Define electric field strength.

Calculate the magnitude of the electric field strength.

field strength = ______ $\text{N C}^{-1}$

Show that the acceleration of the electron in the field is $1.1 \times 10^{16}\ \text{m s}^{-2}$.

Use the acceleration given in (iii) and your answer in (i) to determine the vertical distance $y$ between point B and the upper plate.

$y$ = ______ $\text{cm}$

Explain why the calculation in (iv) does not need to include the gravitational effects on the electron.

The electron enters the field at time $t = 0$.
On Fig. 2.2, sketch graphs to show the variation with time $t$ of

1. the horizontal component $v_X$ of the velocity of the electron,
2. the vertical component $v_Y$ of the velocity of the electron.
   Numerical values are not required.

Define electric field strength.

Calculate the magnitude of the electric field strength.

field strength = ______ $\text{N C}^{-1}$

Show that the acceleration of the electron in the field is $1.1 \times 10^{16}\ \text{m s}^{-2}$.

Use the acceleration given in (iii) and your answer in (i) to determine the vertical distance $y$ between point B and the upper plate.

$y$ = ______ $\text{cm}$

Explain why the calculation in (iv) does not need to include the gravitational effects on the electron.

The electron enters the field at time $t = 0$.

On Fig. 2.2, sketch graphs to show the variation with time $t$ of

1. the horizontal component $v_X$ of the velocity of the electron,
2. the vertical component $v_Y$ of the velocity of the electron.

Numerical values are not required.

Show that the electric force acting on the particle is $4.0 \times 10^{-15}\ \text{N}$.

On Fig. 5.1, draw labelled arrows to show the directions of the two forces acting on the smoke particle.

The resultant force acting on the particle is $F$. Determine

1. the magnitude of $F$,

magnitude = ______ $\text{N}$

1. the angle of $F$ to the horizontal.

angle = ______ $^\circ$

The electric field in (b) is switched on at time $t = 0$ when the particle is at a horizontal displacement $s = 2.0\ \text{cm}$ from the left-hand plate. At time $t = 0$ the horizontal velocity of the particle is zero. The particle is then moved by the electric field until it hits a plate at time $t = T$.

On Fig. 5.2, sketch the variation with time $t$ of the horizontal displacement $s$ of the particle from the left-hand plate.