Q. 435.0( 2 Votes )

# A large conducting plane has a surface charge density 1.0 × 10^{–4} C m^{–2}. Find the electrostatic energy stored in a cubical volume of edge 1.0 cm in front of the plane.

Answer :

Given,

Surface charge density,σ1.0 × 10^{–4} C m^{–2}

Edge length of the cube, e=1.0 cm=0.01m

Permittivity of free space, ε_{0}= 8.85×10^{-12} F/m

__Formula used__

For a conducting plate infinite length), the electric field, E is,

And the electrostatic energy density or the energy per volume is,

Substituting eqn.1 in eqn.2 will result in,

Now the energy stored in volume V is

In the problem, we have to find the force inside a cube of edge e length.

So, we replace V with e^{3} in eqn.3

So,

Now, substituting the known values in the above equation, it becomes,

Or,

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A parallel-plate capacitor has plate area 20 cm^{2}, plate separation 1.0 mm and a dielectric slab of dielectric constant 5.0 filling up the space between the plates. This capacitor is joined to a battery of emf 6.0 V through a 100 kΩ resistor. Find the energy for the capacitor 8.9 μs after the connections are made.

How many time constants will elapse before the energy stored in the capacitor reaches half of its equilibrium value in a charging RC circuit?

HC Verma - Concepts of Physics Part 2