F&W
Tutorial 4
Ques 1. Check, whether
1
V (⃗r) =
4πϵ0
Z
ρ(r⃗′ ) ′
dτ
r
satisfies Poisson’s Equation, by applying the Laplacian and using ∇2
1
= −4πδ 3 (⃗r)
r
Ques 2. An infinite plane slab, of thickness 2d, carries a uniform volume charge density ρ.
Find the electric field, as a function of y only, where y=0 at the center.
⃗ versus y, calling E
⃗ positive when it points in the +y direction and negative
Plot E
when it points in the -y direction.
Figure 1:
Ques 3. A metal sphere of radius R carries a total charge Q. What is the force of repulsion
between the ”northern” hemisphere and the ”southern” hemisphere?
Ques 4. Find the Capacitance per unit length of two coaxial metal cylindrical tubes, of radii a
and b.
1
π
are separated by an infinitesimal
6
π
insulating gap as shown in Figure 2. If V(ϕ = 0)=0 and V(ϕ = )=100V,
6
⃗
Calculate V and E in the region between the planes.
Ques 5. Semi-infinite conducting planes at ϕ = 0 and ϕ =
Figure 2:
2