Question

If linear charge density=surface charge density=volume charge density numerically then the maximum value of charge is on the (a) charged wire (b) charged lamina (c) charged sphere

Answer 1

Explanation:

The charge on the infinitesimal element of length Rdθ is

dQ=λRdθ=λ

0

cos

2

θ

Rdθ

Potential at the center of ring due to charge dQ is

dV=k

R

dQ

=kλ

0

cos

2

θ

dθ

V=∫

0

2π

kλ

0

cos

2

θ

dθ=2kλ

0

[sin

2

θ

]

0

2π

=0

Answer 2

If linear charge density = surface charge density = volume charge density numerically then the maximum value of charge can be on any of the options provided their dimensions are given.

This is because:

1. When different charge densities are numerically equal it means that there is same charge

per length, per area and per volume.

2. So a wire and sphere having same respective charge densities can have more, same or even less total charge depending on the dimensions of each of them.

3. For example: Let numerical charge density be 2 coulumb ( per length, per area and per volume). Now:

• length of wire be 10 m
• area of lamina be 5 m2
• volume of sphere be 3 m3

4. Calculating total charge on :

• Wire = 20 coulumb
• Lamina = 10 coulumb
• Sphere = 6 coulumb

As you can see maximum value of charge depends on the dimensions of respective charge carriers.