A particle of mass 10⁻³ kg and charge 5 µC is thrown at a speed of ...

Question

A particle of mass 10⁻³ kg and charge 5 µC is thrown at a speed of 20 m/s against a uniform electric field of strength 2 × 10⁵ N/C. How much distance will it travel before coming to rest momentarily?

Accepted Answer

Given:
• Mass m = 10⁻³ kg
• Charge q = 5 µC = 5 × 10⁻⁶ C
• Initial speed u = 20 m/s
• Electric field E = 2 × 10⁵ N/C
• Final speed v = 0 (momentarily at rest)

Step 1: Calculate force on the particle
F = qE
F = (5 × 10⁻⁶) × (2 × 10⁵)
F = 1 N

(The particle is moving against the field, so force opposes motion → deceleration)

Step 2: Calculate deceleration
a = F/m
a = 1 / 10⁻³
a = 1000 m/s² (deceleration)

Step 3: Apply third equation of motion
v² = u² - 2as

Step 4: Substitute values
0 = (20)² - 2 × 1000 × s
0 = 400 - 2000s
2000s = 400
s = 0.2 m

Final Answer:
Distance travelled before momentarily coming to rest = 0.2 m = 20 cm

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