Moving Charges and Magnetic Field

A current-carrying conductor produces a magnetic field around it

Step 1: In Oersted's 1820 experiment, a compass needle was placed near a current-carrying wire. Step 2: When current flowed, the needle deflected, showing a magnetic field was created around the wire. Step 3: When current was reversed, the needle deflected in the opposite direction. This proved that moving charges (electric current) produce magnetic fields. Option A is wrong – a stationary charge produces only an electric field, not magnetic. Option C describes electromagnetic induction (Faraday), not Oersted. Option D is also Faraday's law.

μ₀ times the current enclosed by the path

Step 1: Ampere's Circuital Law states: ∮ B·dl = μ₀I, where I is the net current threading through the area enclosed by the closed path. Step 2: μ₀ is the permeability of free space (4π × 10⁻⁷ N A⁻²). Step 3: Only the current enclosed by the chosen path matters, not the total current in the entire circuit. Option B is wrong as ε₀ is the electric permittivity used in Gauss's law for electric fields. Option C is wrong because it says 'total current' not 'enclosed current'. Option D introduces μ₀ε₀ which appears in electromagnetic wave equations.

Zero

Step 1: The magnetic force on a moving charge is given by F = qvB sinθ, where θ is the angle between velocity and magnetic field. Step 2: When the particle moves parallel to the field, θ = 0°. Step 3: F = qvB sin0° = qvB × 0 = 0. The force is zero. The particle moves in a straight line without any deflection. Option A (maximum) corresponds to θ = 90°. Option C gives the maximum force formula. Option D is dimensionally incorrect.

1 N A⁻¹ m⁻¹

Step 1: From the force formula F = qvB sinθ, we can write B = F / (qv sinθ). Step 2: Units of B = Newton / (Coulomb × m/s) = N / (A·s × m/s) = N / (A·m). Step 3: So B = N A⁻¹ m⁻¹. This is also equal to 1 Wb m⁻². Step 4: 1 T = 1 N A⁻¹ m⁻¹ = 1 Wb m⁻². Options B, C, D have incorrect arrangements of the units – in B and D, A appears in numerator (positive power), and in C the length unit is in numerator instead of denominator.