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Question

A uniformly charged conducting sphere of 2.4m diameter has a surface density of 80.0μC/m2. (a) Find the charge on the sphere (b) What is the total electric flux leaving the surface of the sphere?


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Solution

Step 1: Given information

Diameter of the sphere, d=2.4m

The radius of the sphere, r=1.2m

Surface charge density, σ=80.0μC/m2=80×10-6C/m2

Step 2: Finding the charge of the sphere

We know,

The total charge on the surface of the sphere,

Q=Chargedensity×Surfacearea=σ×4πr2

By substituting the values, we get

=80×10-6×4×3.14×(1.2)2=1.447×10-3C

Step 3: Finding the total electric flux leaving the surface of the sphere

We know the relation,

ϕtotal=Qε0

Permittivity of free space, ε0=8.854×10-12N-1C2m-2

Therefore,

ϕtotal=1.447×10-38.854×10-12=1.63×108NC-1m2


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