Unit 3: Electric Force, Field, and Potential

• In an isolated system, the charge is always conserved.

• Protons and electrons have a quality called electric charge.

• The charge is invariant in nature.

• The charge is quantized.

• (Q = n e)

  • e = 1.6 * 10^-19 C

  • n = no. of electrons

  • Q = charge

It involves addition or removal of electrons.

The electric force between two particles with charges q1 and q2 separated by distance r has a magnitude by the equation:

F = Kq1q2/r^2

• F = force

• K = coulomb’s constant

• q1 and q2 = charges

• r = distance between the charges

Consider three point charges: q1, q2, and q3. The total electric force acting on, say, is simply the sum of F1-on-2, the electric force on q2 due to q1, and F3-on-2, the electric force on q2 due to q3:

The space is surrounded by a charge in which another charged particle experiences the force.

E = F on q/ q

It describes the electric field vector from the force vector on a positive charge.

The electric field surrounding the point charge is:

E = 1/4πε0 * Q/r^2

• E = electric field

• Q = charger = distance between charges

• ε0 = permittivity of free space

• Radial field

• It is generated by a collection of point charges.

• An infinite sheet of charge.

• The electric fields follow the same addition properties as the electric force.

• The electric field lines never cross.

A lot of problems deal with the uniform electric field. The field may be taken as uniform at least in the middle. The uniform field just signifies the constant force.

Materials which allow the flow of excess charge without resisting it.

Materials that resist the flow of electrons.

It involves rubbing the insulator against another material, thereby stripping electrons from one to another material.

When we connect two conductors charge flows from one to another until the potential of both the conductors becomes the same.

The process of charging by induction may be used to redistribute charges among a pair of neutrally charged spheres.

There aren’t any free electrons. The atoms make up the sphere will become polarised.

positive

negative

the directions of the electric forces on the charges of mutual interaction; like charges repel, opposite charges attract.

an object with an excess of positive or negative charges

accomplished by Friction, Contact, Induction, or Polarization

Charging by Polarization

By gaining/losing electrons

Conserved

1 e = 1.6 x 10^-19 Coulombs

coulombs

Only the small spot which was directly contacted with a charge remains charged.

semiconductors

two equal and opposite charged

From positive to negative charges ALWAYS

The density of field lines

a weak field

law of conservation of electric charge

We is the work done by the electric force, then the change in the charge’s electrical potential energy is defined by:

Ue = electrical potential energy

We = work done by electric force

Electrical potential energy required to move along the field lines surrounding a point charge is given by:

• q1 and q2 = charges

• e0 = permeability of free space

• Ue = electrical potential energy

• r = distance

Electric potential is the electric potential energy per unit of charge at a point in an electric field, measured in volts (V). It's the work done per unit charge in bringing a test charge from infinity to that point.

V = U/q

Consider the electric field created by a point source charge Q. If a charge moves from a distance rA to a distance rB from Q, then the change in the potential energy is:

• Ub and Ua = electrical potential energies for a and b

• ra and rb = distances for a and b

• e0 = permeability of free space

An equipotential surface is a surface in a region of space where every point on the surface is at the same potential. In other words, no work is required to move a charge along an equipotential surface. Equipotential surfaces are perpendicular to electric field lines and can be used to visualize the electric field in a given region.

V = kQ/r

• V = electric potential energy

• q = point charger = distance between any point around the charge to the point charge

• k = Coulomb constant; k = 9.0 × 109 N

Equipotential curves are curves of constant elevation. If you walk along any of the contour lines and you neither ascend nor descend, then the curve is known as the equipotential curve.

A drawing of several equipotential curves at various values of the potential for a charge distribution is called an equipotential map.

Two conductors, separated by some distance carry equal but opposite charges +Q and -Q. The pair comprises a system called a capacitor.

The capacitor is in the form of parallel metal plates or sheets.

The capacitance measures the capacity for holding charge.

C = κε₀A/d (k = dielectric constant)

Fringing fields extend beyond conductor or magnetic material edges. They weaken as the distance from the edge increases. They're important in device design but can cause interference and affect performance.

The energy stored in a capacitor can be calculated using the formula

Uc = ½QV = ½CV² where

U is the energy stored in joules, C is the capacitance of the capacitor in farads and V is the voltage across the capacitor in volts.

To keep the plates of the capacitor apart they are filled with dielectric which increases the capacitance of the capacitor.

W = q E d

• W = work done

• q = charge

• E = electric field

• d = distance

increases

reciprocal

series

adding

parallel

1 Farad

capacitance

∆V = -Ed

E = -dV/dr

1 J/C

-qEd*cosθ

work

1. Area of the plates (C ∝ A)

2. Distance between the plates ( C ∝ 1/d)

3. Permittivity of medium ( C ∝ ε0)

M-1L-2T4A2

U = -pEcosθ

C = q/V

1. Size and shape of conductor

2. Nature (permittivity)

1/Cs = 1/C1 + 1/C2 + 1/C3

Cp = C1 +C2 + C3