Point and spherical charges (6.2.1)
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Fields are regions where objects will experience a force at a distance. A charged object creates an electric field.
Charged objects experience a force when in an electric field.
An electric field can be created by rubbing a glass rod with a silk cloth, for example. The friction moves electrons from the rod to the cloth, leaving the rod positively charged (due to losing electrons) and the cloth negatively charged.
An electric field surrounds the rod and can attract small pieces of paper or a thin stream of water from a tap:
- The positively charged rod attracts the electrons within the pieces of paper, causing the electrons to shift towards the closer side of the rod. This creates a net attraction between the pieces of paper and the rod.
- Water molecules are said to be polar, meaning they have a slightly positive end and a slightly negative end. This is due to the shape of the molecule and the strong attraction between the electrons and the oxygen atom. When the electric field produced by the rod is brought close by, the negative end of the water molecule aligns with the rod and is attracted towards it. This results in a thin stream of water bending towards the rod as the attraction between the rod and water molecules brings the stream closer.
Electric fields produced by point charges have infinite range. The strength of the electric field due to a point charge follows an inverse square law with the distance from the point charge :
We see that the electric field strength is inversely proportional to the square of the distance from the point charge.
Electric fields from point charges are radial in nature: the field strength decreases radially outwards from the point charge.
Electric field lines are used to specify the direction of the field. Point charges produce radial electric fields.
The field lines point outwards for positive charges and inwards on negative charges.
A point charge and a uniformly charged sphere both produce a radial field. The uniformly charged sphere can be modelled as a point charge at its centre.
The field lines for the uniformly charged sphere (right) are the same as those for the point charge (left) beyond the dashed sphere that represents the edge of the charged sphere.
Due to the point charge and the uniformly charged sphere producing a radial field, we see that the electric field strength decreases with distance from the point charge and the uniformly charged sphere. The image shows that the space between the field lines increases with increasing distance from the point charge and uniformly charged sphere, indicating the field strength is decreasing.
Since the space between the field lines – and therefore the field strength – is decreasing, the field of a point charge and a uniformly charged sphere is non-uniform.
Electric field lines, also known as lines of force, can visualise electric fields. They show the nature of the field created by charges and conductors:
- Arrows show the direction of the field.
- Field lines are always at to the surface.
- A uniform field has field lines that are parallel and equally spaced, i.e. the field strength is the same at all points.
- Field lines that are closer together represent greater field strength.
When two conductors have opposite charges, the electric field lines connect and point from the positive to the negative charge.
Electric fields can have different configurations depending on the size, shape, charge, and arrangement of the objects that produce them.
Uniform field
- A uniform field has equally spaced parallel field lines
- Can be produced between two parallel charged plates
The table below highlights the differences in non-uniform electric fields:
| Feature | Opposite charges | Like charges |
|---|---|---|
| Charge configuration | Two point charges of equal magnitude | Two point charges of equal magnitude, same sign |
| Field-line pattern | Lines emerge from the positive charge and terminate on the negative charge, forming continuous curves between them | Lines emerge from (or terminate on) each charge and curve away from the other; no lines pass directly between the two charges |
| Field at the midpoint (superposition) | Contributions from each charge point in the same direction and add, giving an enhanced field directed from to | Contributions from each charge are equal in magnitude but opposite in direction; they cancel exactly, so the net field is zero |
| Uniformity | Non-uniform: magnitude and direction vary with position; strength falls with distance from each charge | Non-uniform: magnitude and direction vary with position; strength falls with distance from each charge |
| Point of zero net field between the charges | None. The two contributions reinforce everywhere along the axis between the charges | Present at the midpoint (for equal magnitudes). A neutral point |
The electric field strength of an electric field at a point in space is defined as the force per unit charge experienced by a positive test charge at that point. It is a measure of the intensity of the electric field at that point and informs us how much force a positive test charge would experience within that field at that point.
A positive test charge is a hypothetical charge assumed to be positive, used to measure the strength and direction of an electric field at a particular point. It is positive by convention, so that the direction of the electric field lines aligns with the direction a positive charge would move.
The equation for the electric field strength is given by:
Where:
- is the force experienced by the positive test charge,
The unit of electric field strength is the newton per coulomb
The electric field strength is a vector quantity, possessing both magnitude and direction.
By convention, the direction of an electric field at a point in space is the direction a positive charge would move due to a force if placed at that point, as shown in the figure below.
Question walkthrough
Field Strength and Direction from Force on an Electron
Calculates the electric field strength from the force experienced by a moving electron, and determines the direction of the field.