Potential Due to a Point Charge

Answer the following question.
The magnitude of the electric field (in NC ^{– 1}) in a region varies with the distance r(in m) as
E = 10r + 5
By how much does the electric potential increase in moving from point at r = 11 m to a point at r = 10 m.

If a positive charge moves opposite to the direction of the electric field, the field does _______ work on charge and potential energy ________.

The force acting on a particle in one dimension is F = ax - 2xβ³. The corresponding potential energy V(x), assuming V(0) = 0 is given by ______.

A positively charged particle is released from rest in a uniform electric field. The electric potential energy of the charge ______.

The particle P shown in figure has a mass of 10 mg and a charge of −0⋅01 µC. Each plate has a surface area 100 cm² on one side. What potential difference V should be applied to the combination to hold the particle P in equilibrium?

1. The metal plate divides the capacitor into two capacitors connected in parallel to each other.
    
2. The metal plate divides the capacitors into two capacitors connected in series with each other.
    
3. The metal plate is equivalent to a dielectric of zero dielectric constant.

A point charge +Q is placed at point O, as shown in the figure. Is the potential difference V_A – V_B positive, negative or zero?

Show that electric potential at a point P, at a distance 'r' from a fixed point charge Q, is given by:
    `v=(1/(4pi∈_0))Q/r`.