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JEE MainPhysicsMagnetic Effects of Current

An alpha particle is moving along the positive x-axis with a constant velocity v = v₀ i . It enters a region of space containing a uniform electric field E and a uniform magnetic field B . If the particle passes through this region undeflected and without any change in its speed, which of the following pairs of E and B is possible?

Options

  1. AE = E₀ k , B = E₀ v₀ j
  2. BE = E₀ i , B = E₀ v₀ k
  3. CE = 0, B = E₀ v₀ j
  4. DE = E₀ j , B = E₀ v₀ k

Correct answer

D. E = E₀ j , B = E₀ v₀ k

Step-by-step solution

For the alpha particle to pass undeflected with constant velocity, the net Lorentz force on it must be zero. F = q( E + v B ) = 0 E = -( v B ) Given v = v₀ i . Let us check the correct option. If B = E₀ v₀ k , then v B = (v₀ i ) ( E₀ v₀ k ) = -E₀ j . Therefore, E = -(-E₀ j ) = E₀ j . Hence, the pair E = E₀ j and B = E₀ v₀ k produces zero net force. Answer: E = E₀ j , B = E₀ v₀ k

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