## Let us understand About Electric Charge

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

As per the law, creation and destruction of electric charges is not possible.

• The SI unit of electric charge is the coulomb and is denoted by C.
• The charge of an electron used in physics has the value as e = 1.6 × 10-19 Coulomb.
• Therefore, the electron has –e charge, and proton has +e.

### Two Types of Charges exists

1. Positive Charge: They are carried by the protons.
2. Negative Charge: They are carried by the electrons.

## What is Electric Field?

Electric forces define electric fields. The attraction is felt by the charge in a particular surrounding or a field. The electric field is defined everywhere even in free space also. A gravitational field can be considered as an example. Also the water velocity in a river can be considered an example because of the magnitude variation at various places.

## Coulomb’s Law

For force between two minor or small electric charges this statement is stated, the charge considered is either a positive charge or a negative in presence of electric field. When the size of an electric charge is very small in comparison to the separation then at this point the electric charge taken is known as point charge in the electric field. This law states that the force is inversely proportional to the square of distance; also the force is directly proportional to the product of electric charges for that particular. It can be concluded from this statement that

Also for the cases of a sphere if the radius comes out to be smaller than the separation then it is considered as point charges.

## Electric Field

Consider a charge ''Q'' in a medium of vacuum , situated at the origin O. If another charge ‘’q’’ Coulomb is introduced about a point say ‘’P’’, where OP = r, In this case the charge Q will exert a force on ‘’q’’ . Which means that Q is responsible for producing electric fields all around. Also a force will be acting.

## Characteristics of Electric Field Lines

1. Intersection of two electric field lines never exists.
2. The lines are perpendicular to the surface of charge.
3. The proportionality exists between magnitude of charge and the number of electric field lines.
4. At the positive charge, the commencement of lines occurs and for negative charge commencement does not occur.
5. The endpoint of the lines is at the negative charge.

## Electric Flux

If a liquid is flowing with a velocity ‘’v’’, and the surface where it is flowing is ‘’dS’’ this is a small portion considered which is in normal direction. The total liquid that will cross the area will be given as vdS and will represent the flux in the case of liquid. If there is some angle present, let the angle be θ with it, in that case the flux comes out to be v dS cos θ. Similarly this is also applicable for the case of electric field and in case of electric field it will be called as electric flux.

## Electric Dipole

• When the separation between the two point charges is ‘’2a’’ and the charges involved are ‘’-q’’ and ‘’+q’’ this is said to be an electric dipole.
• This distance will be the direction from –q to +q. Here, the total charge will be zero.
• The electric field will not get cancelled when addition is applied but in the situation where r >> 2a, then it nearly cancels out.

### Dipole Electric Field

1. Axis Points

Consider point P at ‘’r’’ distance measured from the center of the dipole on charge ‘’q’’. Then the electric field for the point on-axis is :

${E}_{-q}=\frac{-q}{4\pi \epsilon {\left(r+a\right)}^{2}}$

Where unit vector is considered along –q to +q

Also,

${E}_{+q}=\frac{-q}{4\pi \epsilon {\left(r-a\right)}^{2}}$

The total electric field at P is (r>>a).

$\begin{array}{c}E={E}_{+q}+{E}_{-q}\\ =\frac{q}{4\pi \epsilon }\left(\frac{1}{{\left(r-a\right)}^{2}}-\frac{1}{{\left(r+a\right)}^{2}}\right)\\ =\frac{q}{4\pi \epsilon }\frac{4ar}{{\left({\left(r-a\right)}^{2}\right)}^{2}}\\ =\frac{1}{4\pi \epsilon }\frac{2p}{{r}^{3}}\end{array}$

Where p is the dipole moment and (r>>a)

2. Equatorial Plane Points

For two charges –q and +q electric field magnitude is

${E}_{-q}=\frac{-q}{4\pi \epsilon {\left(r+a\right)}^{2}}$

${E}_{+q}=\frac{-q}{4\pi \epsilon {\left(r-a\right)}^{2}}$

The magnitudes are equal and the directions of electric field E+q and E–q are opposite. Components of the electric field normal to the dipole axis cancel away. The components along the axis add up. The total electric field is opposite to pˆ. We have

$\begin{array}{c}E=-\left({E}_{+q}+{E}_{-q}\right)\mathrm{cos}\theta \\ =\frac{2qa}{4\pi \epsilon {\left({r}^{2}+{a}^{2}\right)}^{\frac{3}{2}}}\\ =-\frac{2qa}{4\pi \epsilon {r}^{3}}\\ =-\frac{p}{4\pi \epsilon {r}^{3}}\end{array}$

Where p is the dipole moment and (r>>a)

## Electrostatic Shielding

The charge gets distributed over the surface of a hollow conductor when placed in an electric field but no electric field is present in the conducting walls thus no electric field presence inside the conductor.

## Difference between Electrostatic and Gravitational Force

Gravitational force is proportional to the mass of interacting objects. Whereas, the electrostatic force is proportional to the magnitudes of the charge of the interacting body.

## Charge Density

Charge density is the amount of electric charge per unit length, surface area, or volume.

## Gauss Law

Gauss law states that for a closed surface the total electric flux passing out of it  is equal to the ratio of charge and the permittivity. The product of the area and the electric field in a plane for a perpendicular direction provides electric flux.

• According to the Gauss law, the total flux linked with a closed surface is numerically equal to 1/ε0 times the enclosed charge over the closed surface.
• $\int E.dA=\frac{q}{{\epsilon }_{0}}$

## Common Mistakes

• The flow of electrons is known as electricity.
• For the condition of frictional electricity, the transference of electrons.
• Do not add charges as real numbers considering it scalar.
• The total charge of an isolated system is always conserved.
• Electrostatic forces are conservative forces.

## Context and Application

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for

• Bachelors in Technology (Mechanical Engineering)
• Masters in Technology (Mechanical Engineering)
• Bachelors in Technology (Civil Engineering)
• Masters in Technology (Civil Engineering)
• Bachelors in Science (Physic)
• Masters in Science (Physics)
• Electric forces
• Electrostatics forces
• Gauss Law

## Practice Problem

Problem : Define a term electric Dipole Moment of a dipole. State its SI unit?

Solution :

• τ=OE sinθ.
if E=1 unit, θ=90º
• then τ=P.

It is defined as the torque acting on an electric dipole, placed perpendicular to a uniform electric field of unit strength Or the strength of an electric dipole is called a dipole moment.

• |P¯|=q|2a|.
• Hence its SI unit is Cm.

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