Magnetic Force Common Exam Traps

Support note: Use this after the teaching notes to check geometry, sign, assumptions and apparatus reasoning.

Overview

Magnetic-force questions are often lost through direction errors rather than formula errors. This support note collects the common traps so that students can check angle definitions, charge signs, force directions, model assumptions and current-balance reasoning.

Core Ideas

• Scalar force formulae use positive magnitudes; sign and direction are handled separately.
• Direction rules require conventional current or positive-charge velocity first.
• Magnetic force is perpendicular to velocity and therefore does no work by itself.
• Circular motion occurs only while the particle remains in the magnetic-field region.
• Electric and magnetic forces have different direction and energy effects.
• Apparatus questions require the active length, correct lever arms and a restored null position.

Exam Relevance

Students should use this note as a final diagnostic checklist after studying Magnetic Force, Charged Particles in Magnetic Fields and Force Between Parallel Currents.

1. Wrong angle

In

$$F=BIL\sin \theta \text{or}F=B|q|v\sin \theta ,$$

$\theta$ is between $\vec{B}$ and conventional current, or between $\vec{B}$ and $\vec{v}$. It is not automatically the angle drawn between the wire and a page edge.

2. Wrong active length

$L$ is the straight conductor length actually within the relevant uniform-field region. Do not use the total circuit length.

3. Saying a zero force has a direction

If the current or velocity is parallel or antiparallel to $\vec{B}$, $F=0$. A zero vector has no defined force direction.

4. Using electron drift as conventional current

For a wire, Fleming’s second finger follows conventional current, opposite to electron drift in a metal.

For a particle, find $\vec{v}\times \vec{B}$ for positive charge and reverse the force for negative charge.

5. Writing a negative force magnitude

Use charge magnitude in scalar equations:

$$F=B|q|v\sin \theta ,r=\frac{mv}{B|q|},T=\frac{2\pi m}{B|q|}.$$

Charge sign controls direction, not the positivity of a magnitude.

6. Claiming magnetic force changes speed

Magnetic force alone is perpendicular to velocity, so it does no work. It can change direction and momentum vector, but not speed, kinetic energy or momentum magnitude.

7. Extending a circular arc outside the field

Circular motion occurs only while the perpendicular magnetic force acts. At a field boundary, the particle leaves tangentially.

8. Confusing electric and magnetic force directions

$${\vec{F}}_E=q\vec{E}.$$

A positive charge is forced along $\vec{E}$; a negative charge is forced opposite $\vec{E}$.

$${\vec{F}}_B=q\vec{v}\times \vec{B}.$$

Magnetic force depends on velocity and is perpendicular to both $\vec{v}$ and $\vec{B}$ when non-zero.

9. Using $v=E/B$ without a direction check

The selector relation applies only when $\vec{E}$, $\vec{B}$ and $\vec{v}$ have the required crossed geometry and the electric and magnetic forces oppose. First check directions, then equate magnitudes.

10. Current-balance mistakes

• Use the force-bearing length inside the field.
• Use perpendicular lever arms from the pivot to each line of action.
• Restore the original null position before using the stated geometry.
• Keep force and moment distinct: $F=BIL$, but moment is $BILd$.
• Convert rider mass to weight $mg$.

11. Parallel-current shortcut without explanation

“Same attracts, opposite repels” is useful recall, but an explanation should identify:

1. the field produced by one wire at the other;
2. the force on the other wire;
3. the equal and opposite partner force.

12. Thinking unequal currents give unequal mutual forces

Both force magnitudes contain the product $I_1{I}_2$. The fields at the two wires may differ, but the mutual forces on equal interacting lengths remain equal and opposite.

13. Cross-product misconception

$\vec{A}\times \vec{B}$ is perpendicular to both $\vec{A}$ and $\vec{B}$. The original vectors $\vec{A}$ and $\vec{B}$ do not have to be mutually perpendicular.

14. Final checklist

• I identified the relevant moving charge or conventional current.
• I used the correct angle and active length.
• I determined direction before applying any negative-charge reversal.
• I used $|q|$ for magnitudes.
• I stated the field/model assumptions.
• I distinguished electric work from magnetic no-work behaviour.
• I checked whether the path should be straight, circular, helical or parabolic.
• In a current balance, I balanced moments about the stated pivot.

Links

• Magnetic Force
• Charged Particles in Magnetic Fields
• Force Between Parallel Currents
• Magnetic Fields
• Electric Fields