The electric potential varies in space according to the relation V = 3 x + 4 y . A particle of mass 10 kg and charge + 1 μ C starts from rest from point (2,3.2) under the influence of this field. Find

Question

The electric potential varies in space according to the relation V = 3 x + 4 y . A particle of mass 10 kg and charge + 1 μ C starts from rest from point (2,3.2) under the influence of this field. Find the velocity (in mm / s ) of the particle when it crosses the x -axis. Assume V and ( x , y ) are in S.I. units.

TestHub · Accepted Answer

E = − ∇ V = − ( 3 i ^ + 4 j ^ ​ ) : uniform, ∣ E ∣ = 5 N/C. The particle moves in a straight line along − 5 3 i ^ + 4 j ^ ​ ​ from (2, 3.2). To reach the x-axis it drops 3.2 m in y, so the path length is s = 3.2 × 4 5 ​ = 4 m. v 2 = 2 a s = 2 m qE ​ s = 2 × 10 1 0 − 6 × 5 ​ × 4 = 4 × 1 0 − 6 ⇒ v = 2 × 1 0 − 3 m/s = 2 mm/s.

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