Question:
The electric field intensity of the center of a charge at a point distance 1m from the centre of the charged sphere of radius 0.25m is 10 to the power of 4 N/C. what is the surface density of the charge on the sphere?
Answer:
Electric field intensity (E) at a distance (d) from the centre of a sphere containing net charge q is given by the relation,
E = q /4πε0 d2
Where, q = Net charge
E is electric field =104 N/C
d = Distance from the centre = 1 m
∈0 = Permittivity of free space
1/4πε0= 9 × 109 N m2 C−2
So, net charge on the sphere, q= E(4πε0)d2
q = 104(1)/9 × 109
q = 0.11×10-5 C
Now, Surface charge density of sphere-
σ =q /Surface Area of sphere
Surface Area of sphere, A = 4πr2
Given, radius r of the sphere= 0.25 m
So, Area A =0.785 m2
Surface charge density, σ =q /Surface Area of sphere
= 0.11×10-5 /0.785 = 1.40×10-6
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