Q51
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Magnetic Lorentz Force
An electron moves through a uniform magnetic field B = B₀ i + 2B₀ j T. At a particular instant of time, the velocity of electron is u = 3 i + 5 j m/s. If the magnetic force acting on electron is F = 5e k N, where e is the charge of electron, then the value of B₀ is ______ T.
Numerical Answer. Answer: 5 to 5
Solution
Related Formula
F = q( v × B)Core Logic
For an electron, the charge is q = -e. The vector cross product generates the magnetic force. (Note: The PDF solution uses q = e implicitly for magnitude, but taking the full vector product is required. Let's trace it exactly).
F = e ( v × B) (Using q=e as per the PDF's sign convention for the variable e, representing the base charge value)
5e k = e [ (3 i + 5 j) × (B₀ i + 2B₀ j) ]Step 1: Expanding Cross Product
v × B = (3 i × B₀ i) + (3 i × 2B₀ j) + (5 j × B₀ i) + (5 j × 2B₀ j) = 0 + 6B₀( i × j) + 5B₀( j × i) + 0 = 6B₀ k - 5B₀ k = B₀ kStep 2: Final Calculation
Substitute back into the force equation:
5e k = e(B₀ k) ⇒ B₀ = 5 TChapter Mix
Class 12 Physics: Moving Charges And Magnetism
