A sideways force changes direction.
A moving charge in a magnetic field experiences force qvB , perpendicular to both velocity and field. Use a right-hand rule for a positive charge and reverse it for a negative one. A parallel velocity component experiences no magnetic force.
Because magnetic force is perpendicular to velocity, it changes direction without doing work on a point charge. For perpendicular entry into a uniform field the path is circular. A current-carrying wire has force BIL , using conventional current direction.
Magnetic force depends on angle
Explore the relationship
Positive charge 1.60 × 10⁻¹⁹ C at 1.00 × 10⁶ m s⁻¹. Magnetic force is perpendicular to velocity.
Tap or focus a plotted point to read its values.
View plotted data as a table
| Series | Angle between v and B / degrees | Force / 10⁻¹⁴ N |
|---|---|---|
| Force / 10⁻¹⁴ N | 0 | 0 |
| Force / 10⁻¹⁴ N | 3 | 0.418688 |
| Force / 10⁻¹⁴ N | 6 | 0.836228 |
| Force / 10⁻¹⁴ N | 9 | 1.25148 |
| Force / 10⁻¹⁴ N | 12 | 1.66329 |
| Force / 10⁻¹⁴ N | 15 | 2.07055 |
| Force / 10⁻¹⁴ N | 18 | 2.47214 |
| Force / 10⁻¹⁴ N | 21 | 2.86694 |
| Force / 10⁻¹⁴ N | 24 | 3.25389 |
| Force / 10⁻¹⁴ N | 27 | 3.63192 |
| Force / 10⁻¹⁴ N | 30 | 4 |
| Force / 10⁻¹⁴ N | 33 | 4.35711 |
| Force / 10⁻¹⁴ N | 36 | 4.70228 |
| Force / 10⁻¹⁴ N | 39 | 5.03456 |
| Force / 10⁻¹⁴ N | 42 | 5.35304 |
| Force / 10⁻¹⁴ N | 45 | 5.65685 |
| Force / 10⁻¹⁴ N | 48 | 5.94516 |
| Force / 10⁻¹⁴ N | 51 | 6.21717 |
| Force / 10⁻¹⁴ N | 54 | 6.47214 |
| Force / 10⁻¹⁴ N | 57 | 6.70936 |
| Force / 10⁻¹⁴ N | 60 | 6.9282 |
| Force / 10⁻¹⁴ N | 63 | 7.12805 |
| Force / 10⁻¹⁴ N | 66 | 7.30836 |
| Force / 10⁻¹⁴ N | 69 | 7.46864 |
| Force / 10⁻¹⁴ N | 72 | 7.60845 |
| Force / 10⁻¹⁴ N | 75 | 7.72741 |
| Force / 10⁻¹⁴ N | 78 | 7.82518 |
| Force / 10⁻¹⁴ N | 81 | 7.90151 |
| Force / 10⁻¹⁴ N | 84 | 7.95618 |
| Force / 10⁻¹⁴ N | 87 | 7.98904 |
| Force / 10⁻¹⁴ N | 90 | 8 |
| Force / 10⁻¹⁴ N | 93 | 7.98904 |
| Force / 10⁻¹⁴ N | 96 | 7.95618 |
| Force / 10⁻¹⁴ N | 99 | 7.90151 |
| Force / 10⁻¹⁴ N | 102 | 7.82518 |
| Force / 10⁻¹⁴ N | 105 | 7.72741 |
| Force / 10⁻¹⁴ N | 108 | 7.60845 |
| Force / 10⁻¹⁴ N | 111 | 7.46864 |
| Force / 10⁻¹⁴ N | 114 | 7.30836 |
| Force / 10⁻¹⁴ N | 117 | 7.12805 |
| Force / 10⁻¹⁴ N | 120 | 6.9282 |
| Force / 10⁻¹⁴ N | 123 | 6.70936 |
| Force / 10⁻¹⁴ N | 126 | 6.47214 |
| Force / 10⁻¹⁴ N | 129 | 6.21717 |
| Force / 10⁻¹⁴ N | 132 | 5.94516 |
| Force / 10⁻¹⁴ N | 135 | 5.65685 |
| Force / 10⁻¹⁴ N | 138 | 5.35304 |
| Force / 10⁻¹⁴ N | 141 | 5.03456 |
| Force / 10⁻¹⁴ N | 144 | 4.70228 |
| Force / 10⁻¹⁴ N | 147 | 4.35711 |
| Force / 10⁻¹⁴ N | 150 | 4 |
| Force / 10⁻¹⁴ N | 153 | 3.63192 |
| Force / 10⁻¹⁴ N | 156 | 3.25389 |
| Force / 10⁻¹⁴ N | 159 | 2.86694 |
| Force / 10⁻¹⁴ N | 162 | 2.47214 |
| Force / 10⁻¹⁴ N | 165 | 2.07055 |
| Force / 10⁻¹⁴ N | 168 | 1.66329 |
| Force / 10⁻¹⁴ N | 171 | 1.25148 |
| Force / 10⁻¹⁴ N | 174 | 0.836228 |
| Force / 10⁻¹⁴ N | 177 | 0.418688 |
| Force / 10⁻¹⁴ N | 180 | 9.79717e-16 |
Explore: Change the angle through 0°, 90° and 180°. Find where force is zero and maximal.
A 0.20 m wire carries 3 A perpendicular to a 0.50 T field.
- F = BIL sin 90°.
- F = 0.50 × 3 × 0.20 = 0.30 N.
Assumed knowledge
Centripetal force and sine.
Learning checkpoints & source
YOUR LEARNING CHECKPOINT- Calculate magnetic force on charges and wires.
- Explain circular charged-particle motion.