Electric Fields

Define electric potential at a point.

Show that the electric potential $V$ at point P when $x = 10\ \text{pm}$ is equal to $130\ \text{V}$.

Calculate, to two significant figures, $V$ when $x = 30\ \text{pm}$.

$V$ = ______ $\text{V}$

On Fig. 5.1, draw a cross ($\times$) at one position, other than infinity, where the electric potential is zero.

On Fig. 5.2, sketch the variation of $V$ with $x$ between $x = 10\ \text{pm}$ and $x = 110\ \text{pm}$.

Define electric potential at a point.

Show that the electric potential $V$ at point P when $x = 10\ \text{pm}$ is equal to $130\ \text{V}$.

Calculate, to two significant figures, $V$ when $x = 30\ \text{pm}$.

$V$ = ______ $\text{V}$

On Fig. 5.1, draw a cross ($\times$) at one position, other than infinity, where the electric potential is zero.

On Fig. 5.2, sketch the variation of $V$ with $x$ between $x = 10\ \text{pm}$ and $x = 110\ \text{pm}$.

Explain why the electric potential near an isolated proton is positive.

On Fig. 5.1, draw an arrow at point Q to show the direction of the electric field at that point.

On Fig. 5.2, sketch the variation of the electric field $E$ at point P with $x$ for values of $x$ between $x = -3R$ and $x = 3R$. Do not include the region inside the sphere between $x = -R$ and $x = R$.

The proton and the electron in a hydrogen atom are separated by a distance of $5.3 \times 10^{-11}\ \text{m}$.

Calculate the electric potential energy of the proton and the electron.

electric potential energy = ______ $\text{J}$

Define electric field.

On Fig. 5.1, draw four field lines to represent the electric field between the plates.

Determine the strength $E$ of the electric field between the plates.

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

An electron travels at a speed of $2.6 \times 10^7\ \text{m s}^{-1}$ towards the region between the plates, as shown in Fig. 5.1.

On Fig. 5.1, draw the path of the electron as it moves between and beyond the plates.

Determine the direction of the uniform magnetic field.

Explain, with reference to the forces exerted by the two fields on the electron, why the path of the electron is undeviated.

Determine the flux density $B$ of the uniform magnetic field. Give a unit with your answer.

$B$ = ______ unit ______

Define electric potential at a point.

Two isolated charged metal spheres X and Y are near to each other in a vacuum. The centres of the spheres are $1.2\ \text{m}$ apart, as shown in Fig. 5.1.

Point P is on the line joining the centres of spheres X and Y and is at a variable distance $x$ from the centre of X.

Fig. 5.2 shows the variation with $x$ of the total electric potential $V$ due to the two spheres.

State three conclusions that may be drawn about the spheres from Fig. 5.2. The conclusions may be qualitative or quantitative.

A proton is held at rest on the line joining the centres of the spheres in (b) at the position where $x = 0.60\ \text{m}$.

The proton is released.

Describe and explain, without calculation, the subsequent motion of the proton.

State the relationship between electric field and electric potential.

Two charged isolated insulating spheres X and Y are near to each other, as shown in Fig. 5.1.

$P$ is a point on the line joining the centres of the spheres.

Explain why it is not possible for the total electric potential and the resultant electric field to simultaneously be zero at point $P$.

Show that the distance $y$ of point $P$ from the centre of sphere Y is equal to $2x$.

State an expression, in terms of $Q$, $x$ and the permittivity of free space $\epsilon_0$, for the electric field strength $E_X$ at $P$ due to sphere X.

$E_X$ = ______

Determine an expression, in terms of $Q$, $x$ and $\epsilon_0$, for the resultant electric field strength $E$ at point $P$ due to the two spheres.

$E$ = ______

State Coulomb’s law.

Fig. 6.1 shows an isolated hollow conducting sphere that is positively charged.

On Fig. 6.1, draw field lines to represent the electric field outside the sphere.

Determine the radius, in cm, of the sphere.

radius = ______ $\text{cm}$

Calculate the charge on the sphere.

charge = ______ $\text{C}$

Suggest an explanation for the fact that the electric field inside the sphere is zero.

State the relationship between electric field and electric potential.

Two charged isolated insulating spheres X and Y are near to each other, as shown in Fig. 5.1.

$P$ is a point on the line joining the centres of the spheres.

Explain why it is not possible for the total electric potential and the resultant electric field to simultaneously be zero at point $P$.

Show that the distance $y$ of point $P$ from the centre of sphere Y is equal to $2x$.

State an expression, in terms of $Q$, $x$ and the permittivity of free space $\varepsilon_0$, for the electric field strength $E_X$ at $P$ due to sphere X.

$E_X$ = ______

Determine an expression, in terms of $Q$, $x$ and $\varepsilon_0$, for the resultant electric field strength $E$ at point $P$ due to the two spheres.

$E$ = ______

State Coulomb’s law.

On Fig. 4.2, draw and label all the forces acting on sphere Y.

Determine the mass of sphere Y.

mass = ______ $\text{kg}$

Calculate the total electric potential energy stored between X and Y.

energy = ______ $\text{J}$

State the direction of the electric force on the electron when between the plates.

Determine the magnitude of the force acting on the electron due to the electric field.

force = ______ $\text{N}$

Explain why the electron does not follow a circular path.

Define electric potential at a point.

Two isolated charged metal spheres X and Y are situated near to each other in a vacuum with their centres a distance of $24\ \text{m}$ apart. Point P is at a variable distance $x$ from the centre of sphere X on the line joining the centres of the spheres.

Fig. 5.1 shows the variation with $x$ of the electric potential $V$ due to the spheres at point P.

State three conclusions that can be drawn about the spheres from Fig. 5.1. The conclusions may be qualitative or quantitative.

1 ______

2 ______

3 ______

A positively charged particle is placed at point P in (b), such that $x = 12\ \text{m}$. The particle is released.

Describe and explain the subsequent motion of the particle.