Example 1 · level 1
A straight wire 0.1 m long carrying 4 A lies at 90° to a uniform magnetic field of 0.5 T. Find the magnetic force on it (in N, correct to 2 decimal places).
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- F = 0.5 × 4 × 0.1 × sin 90° = 0.2 N.
Answer: 0.2 N
CLASS 11–12 PHYSICS · MOVING CHARGES AND MAGNETISM
Magnetic force on a moving charge and a wire
Force on a charge: F = qvB sinθ. On a wire: F = BIL sinθ. A charged particle moving perpendicular to B goes in a circle of radius r = mv/(qB).
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Worked examples
Example 2 · level 2
A proton (q = 1.6 × 10⁻¹⁹ C) moves at 5 × 10⁶ m/s perpendicular to a 0.1 T magnetic field. Find the magnetic force on it in units of 10⁻¹⁴ N (e.g. type 8 for 8 × 10⁻¹⁴ N), correct to 2 decimal places.
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- F = 1.6 × 5 × 0.1 × 10⁻¹³ N = 0.8 × 10⁻¹³ N = 8 × 10⁻¹⁴ N.
Answer: 8
Example 3 · level 3
A proton (m = 1.67 × 10⁻²⁷ kg, q = 1.6 × 10⁻¹⁹ C) enters a 0.2 T magnetic field at 2 × 10⁶ m/s, perpendicular to the field. Find the radius of its circular path in cm (correct to 2 decimal places).
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- r = mv/(qB) = 3.34 × 10⁻²¹ ÷ (1.6 × 10⁻¹⁹ × 0.2)
- = 0.1 m ≈ 10.44 cm.
Answer: 10.44 cm