Electromagnetism
Electromagnetism studies magnetic fields and the force a magnetic field exerts on a moving charge. The PMDC MDCAT 2026 syllabus highlights three areas: magnetic flux density, magnetic flux, and the motion of a charged particle in a magnetic field. Expect 1-2 MCQs per paper.
Magnetic Flux Density
The magnetic flux density B (also called the magnetic field strength) at a point measures the strength of the magnetic field there. It is defined through the force felt by a charge q moving with speed v perpendicular to the field:
B = F / (qv)
So B is the force per unit charge per unit velocity. It is a vector quantity, directed along the field line at that point.
| Form | Expression | Comment |
|---|---|---|
| SI unit | tesla (T) | Named after Nikola Tesla |
| From force on a charge | 1 T = 1 N C−1 (m s−1)−1 | B = F/(qv) |
| Equivalent | 1 T = 1 N A−1 m−1 | Since 1 C s−1 = 1 A |
| Base units | 1 T = 1 kg s−2 A−1 | Useful for dimension questions |
| From flux | 1 T = 1 Wb m−2 | B = Φ/A — "flux density" |
| CGS unit | 1 T = 104 gauss | Earth's field ≈ 5 × 10−5 T |
Magnetic Flux
The magnetic flux through a surface is the total number of field lines crossing it:
Φ = B · A = BA cosθ
where θ is the angle between B and the area vector (normal to the surface). SI unit: weber (Wb); 1 Wb = 1 T m2.
- If the surface is perpendicular to B (θ = 0), Φ is maximum: Φ = BA.
- If parallel to B (θ = 90°), Φ = 0.
- For a coil of N turns, flux linkage = NΦ.
Motion of Charged Particle in Magnetic Field
A charge q moving with velocity v in a magnetic field B feels the Lorentz force:
F = q v × B |F| = qvB sinθ
The force is always perpendicular to v, so it changes direction but not speed. Magnetic forces do no work on a free charge.
Three special cases
- v parallel to B: F = 0. The charge moves in a straight line; B has no effect.
- v perpendicular to B: The force provides centripetal acceleration. The charge moves in a circle.
- v at an angle to B: The component along B is unchanged; the perpendicular component drives circular motion. Result: a helical path.
Circular motion — key formulas
For v perpendicular to B, equating qvB to mv2/r:
r = mv/(qB)
The angular frequency and period are
ω = qB/m, T = 2πm/(qB) = 2π/ω
Crucially, both ω and the period T are independent of v: a faster particle traces a bigger circle but takes exactly the same time to go round it.
Worked MCQs
Five MCQs that capture the high-yield testing patterns for this chapter. Read the explanation even when you get the answer right — it's where the deeper concept lives.
Q1. A charged particle moving in a uniform magnetic field experiences a force that is:
F = q v × B. The cross-product is perpendicular to both v and B, so the force never does work and the speed stays constant. The force is maximum when v is perpendicular to B and zero when parallel.
Q2. The radius of the circular path of a charged particle in a magnetic field is given by:
qvB = mv2/r ⇒ r = mv/(qB). The period T = 2πm/(qB) is independent of v — same time for any speed, just different circles.
Q3. SI unit of magnetic flux is:
Flux Φ is measured in webers (Wb = T m2). Flux density B is measured in teslas. Henry is the unit of inductance; gauss is a CGS unit (104 G = 1 T).
Q4. A square coil of side 0.20 m is placed with its plane perpendicular to a uniform magnetic field of 0.50 T. The magnetic flux through the coil is:
Area A = 0.20 × 0.20 = 0.040 m2. The plane is perpendicular to B, so the area vector is parallel to B and θ = 0: Φ = BA cos0 = 0.50 × 0.040 = 0.020 Wb. Flux would be zero only if the plane contained the field lines.
Q5. An electron and a proton enter the same magnetic field perpendicularly with the same kinetic energy. Which has the smaller circular radius?
Same KE: mv2/2 same, so mv = √(2mE). Therefore r = mv/(qB) = √(2mE)/(qB) ∝ √m. Electron has smaller mass, hence smaller radius. (Charges have equal magnitude.)
Quick Recap
- Magnetic flux: Φ = BA cosθ (Wb).
- Flux density B = F/(qv), measured in tesla; 1 T = 1 N A−1 m−1 = 1 Wb m−2.
- Lorentz force: F = qv × B; magnitude qvB sinθ; does no work.
- v ⊥ B ⇒ circle of radius r = mv/(qB); period T = 2πm/(qB), independent of v.
- v at angle to B ⇒ helical motion; v parallel to B ⇒ no force at all.