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A 1.0-mm-diameter oil droplet (density role="math" localid="1649088632675" 900kg/m3 ) is negatively charged with the addition of 25 extra electrons. It is released from rest 2.0mm from a very wide plane of positive charge, after which it accelerates toward the plane and collides with a speed of 3.5m/s. What is the surface charge density of the plane?

Short Answer

Expert verified

The surface charge density of the plane is6.4x10-6C/m²

Step by step solution

01

Given information and formula used

Given :

Diameter of oil droplet : 1.0-mm

Density : 900kg/m3

Charge : Negatively charged with 25extra electrons.

It is released from rest : 2.0mm

Collides with a speed of : 3.5m/s.

Theory used :

Conservation of Energy says :

12mv2=qEd

02

Calculating the surface charge density of the plane 

Mass of the droplet is :

ρ×43πr3=900×43π×(0.5×10-6)3=4.7x10-16kg

Mass charge on the droplet :

ne=25×1.6×10-19=40×10-19C

From energy conservation :

E=12×mv²qd=12×4.7×10-16×(3.5)240×10-19×2×10-3=3.6x105N/C

We know that for electric field owing to infinite plane sheet:

E=η2ε0η=E2ε0=2×8.85×10-12×3.6×105=6.4x10-6C/m²

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