30.3 Content
30.3.1 Uniform Electric Field Between Parallel Plates
A uniform electric field exists between parallel plates with potential difference \(V\) and separation \(d\):
\[E = \frac{V}{d}\]
where: - \(E\) = electric field strength (N/C or V/m) - \(V\) = potential difference (V) - \(d\) = plate separation (m)
- Field is uniform (constant magnitude and direction)
- Field lines are parallel, equally spaced
- Force on a charge is constant throughout the field
30.3.2 Interactive: Charged Particle in Electric Field
Visualise the motion of charged particles between parallel plates:
30.3.3 Force and Acceleration in Electric Fields
A charged particle experiences a force:
\[F = qE\]
By Newton’s second law:
\[a = \frac{qE}{m}\]
In a uniform electric field, charged particles follow parabolic paths—identical to projectile motion in a gravitational field. The key difference: \(a = qE/m\) instead of \(g\).
30.3.4 Work and Energy
Work done on a charge moving through potential difference:
\[W = qV = qEd\]
This equals the change in kinetic energy:
\[qV = \frac{1}{2}mv^2 - \frac{1}{2}mv_0^2\]
For a particle starting from rest:
\[v = \sqrt{\frac{2qV}{m}}\]
30.3.5 Interactive: Energy Gain Across Plates
30.3.6 Magnetic Force on Moving Charges
A charged particle moving through a magnetic field experiences a force:
\[F = qvB\sin\theta\]
where: - \(F\) = magnetic force (N) - \(q\) = charge (C) - \(v\) = velocity (m/s) - \(B\) = magnetic field strength (T) - \(\theta\) = angle between \(\vec{v}\) and \(\vec{B}\)
- The force is perpendicular to both velocity and field
- No force when \(v \parallel B\) (θ = 0° or 180°)
- Maximum force when \(v \perp B\) (θ = 90°)
- The magnetic force does no work (always perpendicular to motion)
30.3.7 Interactive: Charged Particle in Magnetic Field
30.3.8 Circular Motion in Magnetic Fields
For motion perpendicular to \(B\), the magnetic force provides centripetal force:
\[qvB = \frac{mv^2}{r}\]
Solving for radius:
\[r = \frac{mv}{qB}\]
- Larger mass → larger radius (heavier particles curve less)
- Larger velocity → larger radius (faster particles curve less)
- Larger field → smaller radius (stronger field bends more)
- Radius is independent of entry point (depends only on \(m\), \(v\), \(q\), \(B\))
30.3.9 Comparing Electric and Magnetic Fields
| Property | Electric Field | Magnetic Field |
|---|---|---|
| Force direction | Along field (+ charge) | Perpendicular to v and B |
| Force on stationary charge | Yes (\(F = qE\)) | No |
| Work done | Yes (\(W = qV\)) | No |
| Trajectory | Parabolic | Circular (if v ⊥ B) |
| Speed change | Yes | No |