7.3.4

# Electric Potential

Test yourself

## Electric Potential

Electric potential is the work done to move a positive test charge from infinity to a given point within the field.

### Work done

• Electric potential is the work which you need to do to bring a positive point charge to a distance, r, from the charge making the field.
• The potential at infinity is zero.
• The potential is largest right next to the charge.

### Calculating the potential

• Electric potential = constant x charge ÷ distance
• $V=\frac{1}{4{\pi}{{\epsilon}_0}}{\times}\frac{Q}{r}$
• Potential is proportional to $\frac{1}{r}$ so falls off more slowly than force or field

## Moving in an Electric Field

In order to move a charge through a field, work must be done as the energy of the charge will change.

### Equipotentials

• An equipotential line or surface is one on which the voltage is constant.
• This means that there is no change in potential difference or energy if a charge just moves along this line or surface.
• No work is done if a charge moves along an equipotential.
• Equipotential lines are placed at equal intervals of energy

### Point charge equipotential

• For a charge equipotential lines are circles of constant radius.
• As the lines get further from the charge the gaps between the lines get larger .

### Parallel plate equipotential

• For parallel plates, equipotential lines are straight lines parallel to the plates.
• These straight lines are evenly spaced as the field is uniform.

### Work done

• Work done to move a charge = charge x change in potential difference
• $W=Q{\Delta}V$
• If the charge is moved between equipotential lines then work is done.
• ${\Delta}V$ can be found by finding the area under a field-distance graph.

## Electric Potential Graph

Gravitational potentials and electrostatic potentials have very similar graphs.

### Comparison to gravitational potential

• The gravitational field strength around a point mass and the electrostatic field around a point charge have the same patterns, although they are different magnitudes.
• The formulae for the relationship between the field strength and distance both include inverse-squares.
• The significant difference is that electrostatic fields can have either positive or negative values, indicating that the force can either be repulsive or attractive respectively.

### Calculating work done

• Just like in the gravitational case, the work done in moving a positive charge away from a central positive charge can be calculated by finding the area underneath the appropriate curve.

### Positive or negative charge

• The electrostatic potential-distance graphs mirror those of the gravitational potential-distance graphs.

### Positive or negative charge 2

• In both cases, the magnitude of the electrostatic potential is given by:
• $V=\frac{Q}{4\pi \epsilon_0 r}$