The Motor Effect
This topic covers the motor effect, where a wire carrying a current within a magnetic field experiences a force. This principle is fundamental to understanding how DC electric motors convert electrical energy into kinetic energy.
Part of the ESAT Physics syllabus — revision for the Engineering and Science Admissions Test (ESAT), the UAT-UK admissions test for Cambridge, Imperial, Oxford and UCL.
Key points
- A force acts on a current-carrying wire in a magnetic field unless the wire is parallel to the field lines. The force is maximum when the wire and field are perpendicular.
- The direction of the force is perpendicular to both the magnetic field and the current. Use Fleming's Left-Hand Rule to determine this direction.
- Reversing the direction of EITHER the current OR the magnetic field will reverse the direction of the force. Reversing both results in no change to the force's direction.
- The magnitude of the force is proportional to the magnetic field strength (B), the current (I), and the length of the wire in the field (L).
- A DC motor uses a coil in a magnetic field. A split-ring commutator reverses the current's direction in the coil every half-turn, ensuring continuous rotation in one direction.
Diagram
› Why does this happen?
Why does the magnetic field create a force?
An electric current is a flow of charged particles (electrons). Any moving charge creates its own magnetic field. So, a current-carrying wire acts like a temporary, thin electromagnet, with circular magnetic field lines around it.
When you place this wire in the field of a permanent magnet, the two magnetic fields interact. On one side of the wire, the two fields are in the same direction and add together, creating a stronger magnetic field. On the other side, they are in opposite directions and partially cancel out, creating a weaker field. This imbalance in field strength results in a force that pushes the wire from the stronger field area towards the weaker field area. This push is the motor effect force.
Why does F = B I L explain the force's size?
The formula F = B I L shows what makes the force bigger or smaller.
- A stronger magnetic field (larger B) provides a stronger external field to interact with, so the resulting push is bigger.
- A larger current (larger I) means more electrons are flowing, creating a stronger magnetic field around the wire. This stronger wire-field results in a bigger interaction and a bigger force.
- A longer wire in the field (larger L) means more of the current is interacting with the magnetic field. The total force is the sum of the small forces on all the moving charges within the field, so a longer wire experiences a greater total force.
How does a commutator keep a motor spinning?
A simple coil in a magnetic field would rotate for half a turn. After this point, the force on each side of the coil would start to oppose the rotation, trying to push it back the way it came. This means the coil would just wobble back and forth instead of spinning continuously. To get continuous rotation, the turning effect must always push the coil around in the same direction.
The split-ring commutator is a clever switch. Just as the coil passes the vertical position, the commutator reverses the direction of the current flowing into the coil. According to Fleming's Left-Hand Rule, reversing the current reverses the force. This reversal happens at the exact right moment to ensure the force on each side of the coil keeps pushing it in the same circular direction, producing continuous rotation.
Formulae
F = B I L To calculate the magnitude of the force (F) on a straight wire of length (L) carrying a current (I), when the wire is at a right angle (90°) to a uniform magnetic field of strength (B).
Definitions
- Motor Effect
- The phenomenon where a force is exerted on a conductor carrying an electric current when it is placed within an external magnetic field.
- Fleming's Left-Hand Rule
- A mnemonic for finding the direction of the force in the motor effect. The Thumb represents Force, the First finger represents the magnetic Field (North to South), and the Second finger represents the conventional Current (+ to -).
- Magnetic Field Strength (B)
- A measure of the intensity of a magnetic field, expressed in Tesla (T). 1 Tesla is the field strength that produces a force of 1 Newton on a 1 metre wire carrying a 1 Amp current.
Worked example
A straight wire of length 40 cm is placed inside a uniform magnetic field of 0.2 T, at right angles to the field lines. A force of 0.6 N acts on the wire. Calculate the current flowing through the wire.
- 1
Recall the formula for the motor effect:
F = B I L - 2
Rearrange the formula to solve for current (I):
I = F / (B × L) - 3
Convert the length from centimetres to SI units (metres):
40 cm = 0.4 m - 4
Substitute the given values into the rearranged formula:
I = 0.6 / (0.2 × 0.4) - 5
Calculate the product in the denominator:
0.2 × 0.4 = 0.08 - 6
Perform the final division:
I = 0.6 / 0.08This is equivalent to 60 / 8, which simplifies to 30 / 4, or 15 / 2.
- 7
The final result is I = 7.5 A.
Answer: 7.5 A
Common mistakes
- ×Forgetting to convert length from centimetres to metres before using F = BIL. All quantities in the formula must be in standard SI units (N, T, A, m).
- ×Incorrectly applying the Left-Hand Rule. A common mistake is pointing the second finger in the direction of electron flow instead of conventional current (from positive to negative).
- ×Making errors in decimal multiplication or division. For example, confusing 0.2 × 0.4 = 0.08 with 0.8.
- ×Misinterpreting diagrams showing current direction. A dot (⊙) indicates current coming out of the page, while a cross (⊗) indicates current going into the page.
No-calculator tips
- ✓To handle decimal calculations in F = BIL, convert them to fractions or use powers of ten. For example, 0.6 / (0.2 × 0.4) can be seen as (6 x 10-1) / (2 x 10-1 × 4 x 10-1) = 6 / (2 × 4 × 10-1) = 6 / 0.8 = 60 / 8 = 7.5.
- ✓When dividing by a decimal, multiply the top and bottom of the fraction by a power of 10 to make the denominator a whole number. For 0.6 / 0.08, multiply both by 100 to get 60 / 8.
- ✓When multiplying a set of numbers, look for combinations that create integers first. For I = 4 A, B = 0.25 T, L = 0.5 m, calculate (4 × 0.25) first to get 1, then multiply by 0.5 to get F = 0.5 N.