Point and spherical charges — OCR A-Level Physics
Test yourself on Point and spherical charges with OCR A-Level practice questions.
7 days Premium · Then free forever · No card, no charge
Point and spherical charges explained
An electric field is a region in which a charged object experiences a force, and the field exists because charge is present.
Read the full explanation
Charge is the source of the field: a positive charge sets up a field pointing radially away from it, while a negative charge sets up a field pointing radially towards it. Field strength falls with distance from the source charge, so the field is strongest close to the charge. A useful method is to sketch the field around a single isolated charge first, then add a second charge and combine the two fields by superposition. In this section you meet point and spherical charges, so treat the source as a point charge at the centre of a uniformly charged sphere.
(b) modelling a uniformly charged sphere as a point charge at its centre
A uniformly charged sphere has its charge spread evenly over its surface or volume. Outside the sphere, the field it produces is identical to that of a point charge of the same total charge placed at the sphere's centre. This lets you use the point-charge field equation for any distance r greater than the sphere's radius R. Inside a uniformly charged insulating sphere the field behaves differently and is not simply that of a central point charge, so the model applies only outside the sphere. A reliable method is to check the distance from the centre: if r is greater than R, use the point-charge model; if r is less than R, do not.
(c) electric field lines to map electric fields
Electric field lines are a visual way to represent an electric field. The direction of a field line at any point gives the direction of the force on a positive test charge there. The spacing of the lines indicates field strength: closely spaced lines mean a strong field, widely spaced lines mean a weak field. Field lines start on positive charges and end on negative charges, and they never cross. To map a field, draw lines with arrows showing direction and vary their spacing to show how strength changes with position. For a point charge the lines are radial and evenly spaced in angle, becoming further apart with distance.
(d) electric field strength; E = F/q.
Electric field strength E at a point is defined as the force F per unit positive charge q placed at that point, giving E = F/q. The unit is newtons per coulomb, N C⁻¹, which is equivalent to volts per metre, V m⁻¹. Rearranging gives F = Eq, so a charge q in a field E experiences a force Eq. Field strength is a vector, so direction matters: the force on a positive charge is in the direction of E, while the force on a negative charge is opposite to E. A reliable method is to identify the charge sign first, then use E = F/q to find magnitude and decide direction from the sign.
Your focus
- State that electric fields arise from electric charges.
- Determine the direction of the electric field around positive and negative point charges.
- Describe how field strength varies with distance from a point charge.
Show all 12 objectives
- State the conditions under which a uniformly charged sphere can be modelled as a point charge.
- Apply the point-charge model to calculate fields outside a charged sphere.
- Recognise when the point-charge model is not valid.
- Draw electric field lines for simple charge configurations.
- Interpret field line diagrams to determine field direction and relative strength.
- State the rules governing electric field lines.
- Define electric field strength using E = F/q.
- Calculate the force on a charge placed in a known electric field.
- Determine the direction of the force on positive and negative charges in an electric field.
Point and spherical charges exam tips
Marking Points
- Electric fields are produced by electric charge; without a source charge there is no field.
- The direction of the field depends on the sign of the source charge: away from positive, towards negative.
- Field strength decreases with increasing distance from the source charge.
- For a uniformly charged sphere the field outside can be modelled as that of a point charge at the centre.
- Superposition: the resultant field at a point is the vector sum of the fields due to each source charge.
- A uniformly charged sphere can be modelled as a point charge at its centre for points outside the sphere.
- The total charge of the sphere is treated as concentrated at the centre in this model.
- The model is valid only for distances greater than the sphere's radius.
- Inside a uniformly charged insulating sphere the field is not given by the point-charge model.
- The model allows the field equation for a point charge to be applied to a spherical charge distribution.
- Field lines show the direction of the electric field at each point.
- The arrow on a field line points in the direction of the force on a positive test charge.
- Closer spacing of field lines indicates a stronger field; wider spacing indicates a weaker field.
- Field lines begin on positive charges and end on negative charges.
- Field lines never cross each other.
- Electric field strength is defined as force per unit positive charge: E = F/q.
- The unit of electric field strength is N C⁻¹, equivalent to V m⁻¹.
- Rearranging gives F = Eq, the force on a charge q in a field E.
- Field strength is a vector; its direction is the direction of the force on a positive charge.
- For a negative charge the force is opposite to the field direction.
Examiner Tips
- 💡Read the stem carefully and identify the sign of each source charge before choosing an option.
- 💡Eliminate options that describe field direction incorrectly for the given charge sign.
- 💡Check whether the question asks about the field due to one charge or the resultant field due to several charges.
- 💡Check whether the point of interest is inside or outside the sphere before selecting an option.
- 💡Remember the model uses the total charge of the sphere, not a fraction of it.
- 💡If the question mentions a uniformly charged sphere, look for the condition r greater than R.
- 💡Always include arrows on field lines in your diagrams.
- 💡Use spacing to convey relative field strength, not just the number of lines.
- 💡Check that no two field lines cross before finalising your sketch.
- 💡Write down the definition of E before substituting values.
- 💡Check the sign of the charge to determine the direction of the force.
- 💡Remember N C⁻¹ and V m⁻¹ are equivalent units for field strength.
Common Mistakes
- Thinking a field can exist without a source charge; correct this by always identifying the charge that sets up the field.
- Believing field lines point towards a positive charge; correct this by remembering field direction is the force on a positive test charge, so lines point away from positive and towards negative.
- Assuming field strength is the same everywhere around a point charge; correct this by noting it falls with distance from the charge.
- Treating electric field as a scalar; correct this by adding fields as vectors when more than one source charge is present.
- Applying the point-charge model inside the sphere; correct this by restricting the model to points outside the sphere.
- Forgetting that the sphere's total charge, not surface charge density, is used in the model; correct this by using the total charge Q.
- Assuming the model works for any shape of charged object; correct this by noting it applies to uniformly charged spheres.
- Confusing the sphere's radius with the distance from the centre; correct this by using r for the distance from the centre and R for the radius.
- Drawing field lines that cross; correct this by ensuring lines never intersect because the field has only one direction at each point.
- Using uniform spacing for a point charge; correct this by increasing spacing with distance to show weakening field.
- Omitting arrows; correct this by adding arrows that show the direction of the field.
- Drawing field lines that start or end in empty space; correct this by starting them on positive charge and ending them on negative charge.
- Using the charge magnitude without considering sign when determining force direction; correct this by noting the force on a negative charge is opposite to E.
- Confusing E = F/q with E = kQ/r²; correct this by recognising the first is the definition and the second applies to a point charge in a vacuum.
- Forgetting that q in E = F/q is the test charge, not the source charge; correct this by identifying which charge experiences the force.
- Treating field strength as a scalar; correct this by remembering it has direction as well as magnitude.