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A charge ( - q ,   m ) is projected with an initial velocity v 0 in the direction of a unidirectional field E 0 x as shown in the figure. Find the distance covered by the charge before it comes to rest.

Options

  1. Av 0 m q E 0
  2. B2 v 0 m q E 0
  3. Cv 0 m 2 q E 0
  4. Dv 0 2 m q E 0

Correct answer

C. v 0 m 2 q E 0

Step-by-step solution

Since the charge is negative and is projected along the electric field, it will experience a retardation q E 0 m . Let the charge travel a distance s before coming to rest ( v = 0 ) . Using the third equation of motion, v 2 = u 2 + 2 a s u 2 = - 2 a s ⇒   v 0 2 = 2 q E 0 s m ⇒   s = v 0 m 2 q E 0 .

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