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JEE MainPhysicsMagnetic Effects of Current

A particle of mass m and charge q is projected into a region containing a uniform magnetic field described by B = B₀ i . If the initial velocity of the particle is v = v₀ i + v₀ j , what is the magnitude of its initial acceleration?

Options

  1. A2 q v₀ B₀ m
  2. Bq v₀ B₀ m
  3. C0
  4. D2 q v₀ B₀ m

Correct answer

B. q v₀ B₀ m

Step-by-step solution

The magnetic force on a moving charge is given by F = q( v B ) . Substituting the given vectors: F = q((v₀ i + v₀ j ) B₀ i ) Using the properties of cross products, i i = 0 and j i = - k . F = q(v₀ B₀ ( i i ) + v₀ B₀ ( j i )) = -q v₀ B₀ k The magnitude of the magnetic force is | F | = q v₀ B₀ . The magnitude of the initial acceleration is a = | F | m = q v₀ B₀ m . Answer: q v₀ B₀ m

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