Electrostatical energy of charged surface in applied voltage

[toni_2374]

Homework Statement

1. Given a coloidal polystyrene particle with a diameter of 350 nm and a surface charge of 7.73. µC cm-2 evaluate: a) the electrostatic energy under and applied voltage of 100 mV

Homework Equations

particle charge density:
ρ = (3Q)/(4πR^3)
U0 =∫V (r)dq

The Attempt at a Solution

V(r)=q(r)/4πε0r
U0 =∫V (r)dq=(4π(ρ^2)R^5)/15ε0

BUT I DO NOT UNDERSTAND APPLIED VOLTAGE WHAT IT MEANS?

 

[gneill]

Homework Statement

1. Given a coloidal polystyrene particle with a diameter of 350 nm and a surface charge of 7.73. µC cm-2 evaluate: a) the electrostatic energy under and applied voltage of 100 mV

Homework Equations

particle charge density:
ρ = (3Q)/(4πR^3)
U0 =∫V (r)dq

The Attempt at a Solution

V(r)=q(r)/4πε0r
U0 =∫V (r)dq=(4π(ρ^2)R^5)/15ε0

BUT I DO NOT UNDERSTAND APPLIED VOLTAGE WHAT IT MEANS?

Hi toni_2374, Welcome to Physics Forums.

Perhaps "applied voltage" means an electric potential of 100mV where the particle is located; perhaps an awkward translation? If so they're probably looking for the electric potential energy associated with that charge being located there.

Also, do you think the polystyrene particle will be uniformly charged throughout its volume, or just on its surface? If just its surface, look carefully at your expression for charge density; what's the expression for the surface area of a sphere?

 

[toni_2374]

yes particle will be uniformly charged on surface,and we consider particle as sphere to be able to use A=4πr^2,HOW should i calculate electric potential energy?

 

[gneill]

Electric potential energy of a charge Q sitting at a location where the electric potential is V is just Q*V. Q is in Coulombs and V is in Volts, which is also Joules/Coulomb

 

[rezeew]

Applied voltage refers to an external electric potential that is applied to the charged surface. In this case, it is a voltage of 100 mV. This voltage causes a change in the electric field around the surface, which in turn affects the electrostatic energy of the charged particle. To calculate the electrostatic energy under this applied voltage, you would need to use the equation you have provided with the given values for the particle diameter and surface charge. This will give you the electrostatic energy of the particle under the influence of the applied voltage.