Revision: Class 12 >> Electric Charges and Fields NEET (UG) Electric Charges and Fields

The basic property of matter due to which it experiences electric force and shows attraction or repulsion, is called electric charge.

Those substances in which electric charge cannot flow are called ‘insulators' (or dielectrics). Glass, hard-rubber, plastics and dry wood are insulators. Insulators have practically no free electrons.

OR

Substances which allow electricity to pass through them easily are called conductors.

Substances whose resistance to the movement of charges is intermediate between conductors and insulators, are called semiconductors.

Conductors are those through which electric charge can easily flow. Metals, human body, earth, mercury and electrolytes are conductors of electricity.

OR

Substances which offer high resistance to the passage of electricity and do not allow electricity to pass through them easily, are called insulators.

The force of attraction or repulsion acting between two electric charges is called the electric force.

The space surrounding an electric charge q in which another charge q₀ experiences a (electrostatic) force of attraction or repulsion, is called the electric field of the charge q.

OR

Electric field due to a charge Q at a point in space may be defined as the force that a unit positive charge would experience if placed at that point.

The region in which the charge experiences an electric force is the electric field around the charge.

“An electric line of force is an imaginary smooth curve drawn in an electric field along which a free, isolated positive charge moves. The tangent drawn at any point on the electric line of force gives the direction of the force acting on a positive charge placed at that point.”

The electric dipole moment is defined as the product of the magnitude of one of the charges and the distance between the two equal and opposite charges.

An electric dipole is a pair of equal and opposite point-charges placed at a short distance apart.

“The line joining the two charges, pointing from the negative charge to the positive charge. This is known as the ‘direction of dipole axis’.”

The charge per unit volume in a region of space, is called volume charge density.

\[\rho=\frac{\Delta Q}{\Delta V}\]

A charge distribution in which charge is treated as continuously spread over a line, surface, or volume (ignoring microscopic discreteness), is called continuous charge distribution.

The charge per unit area on a surface, is called surface charge density.

\[\sigma=\frac{\Delta Q}{\Delta S}\]

The charge per unit length along a line (such as a wire), is called linear charge density.

\[\lambda=\frac{\Delta Q}{\Delta l}\]

\[\vec{E}=\frac{1}{4\pi\varepsilon_0}\frac{Q}{r^2}\hat{r}\]

\[\vec τ\] = \[\vec p\] × \[\vec E\]

Magnitude: τ = pE sin θ

\[\vec{E}=\frac{1}{4\pi\varepsilon_0}\sum\frac{\rho\Delta V}{r^{\prime2}}\hat{r}^{\prime}\]

Gauss' Law states that the net electric flux through any closed surface is equal to `1/epsilon_0` times the net electric charge within that closed surface.

`oint  vec" E".d vec" s" = (q_(enclosed))/epsilon_o`

In the diagram, we have taken a  cylindrical gaussian surface of radius = r and length = l.
The net charge enclosed inside the gaussian surface `q_(enclosed) = lambdal`
By symmetry, we can say that the Electric field will be in radially outward direction.

According to gauss' law,

`oint  vec"E".d  vec"s" = q_(enclosed)/epsilon_o`

`int_1 vec"E" .d  vec"s" + int_2  vec"E" .d  vec"s" + int_3  vec"E". d  vec"s" = (lambdal)/epsilon_o`

`int_1  vec"E". d  vec"s"  &  int_3  vec"E". d  vec"s"  "are zero", "Since"  vec"E"  "is perpendicular to"  d  vec"s"`

`int_2  vec"E" . d  vec"s" = (lambdal)/epsilon_o`

`"at"  2,  vec"E" and d  vec"s"  "are in the same direction, we can write"`

`E.2pirl = (lambdal)/epsilon_o`

`E = lambda/(2piepsilon_o r)`

Statement

The principle of superposition states that the net electric force acting on a given charge due to a number of other charges is equal to the vector sum of the individual forces exerted on it by each charge taken separately, assuming the other charges are absent.

Explanation / Mathematical Form

Consider a system of nnn point charges q₁,q₂,q₃,…,q_n.

The force acting on charge q₁ due to the other charges is:

\[\vec{F}_1=\vec{F}_{12}+\vec{F}_{13}+\cdots+\vec{F}_{1n}\]​

where
\[\vec F_{12}\]​ is the force on q_1​ due to q₂​,
\[\vec F_{13}\]​​ is the force due to q₃​, and so on.

According to Coulomb’s law, the force on q₁​ due to q₂​ is:

\[\vec F_{12}\]​ = \[\frac{1}{4\pi\varepsilon_0}\frac{q_1q_2}{r_{12}^2}\hat{r}_{12}\]​

Similarly, forces due to other charges can be written, and their vector sum gives the resultant force on q₁​.

Thus, the force between any two charges is independent of the presence of other charges.

Conclusion

The principle of superposition shows that:

• Electric forces obey vector addition.
• Each pair of charges interacts independently.
• The net force on a charge in a multi-charge system is found by adding all individual Coulomb forces vectorially.

• Thales (≈2500 years ago) observed that amber rubbed with wool attracts light objects like paper and straw.
• William Gilbert (1600) showed that many materials, such as glass, ebonite, and sulphur, also show this effect.
• This attractive property is produced by rubbing (friction); a material showing it is said to be electrified, and the process is called frictional electricity.
• An electrified material possesses electric charge and is therefore called a charged body.
• Electric charge is quantised (q = ±ne,  e = 1.6 × 10⁻¹⁹ C); there are two types of charges (positive and negative), as charges repel, unlike charges attract, and the SI unit of charge is coulomb (C).

• A charge creates an electric field around it, even if no other charge is present.
• The electric field does not depend on the test charge used to measure it (if the test charge is very small).
• The field of a positive charge points outward; the field of a negative charge points inward.
• The strength of the electric field decreases as the distance from the charge increases.
• At equal distances from a point charge, the electric field has the same magnitude (spherical symmetry).

• Electric field lines originate from positive charges and terminate on negative charges (or at infinity).
• The tangent to a field line at any point gives the direction of the electric field; in a uniform field, the lines are parallel and straight.
• No two electric field lines intersect, as this would imply more than one direction of the electric field at a point.
• Electric field lines do not pass through a conductor, showing that the electric field inside a conductor is zero.
• The density of field lines indicates field strength—closer lines represent a stronger field, while wider spacing represents a weaker field; the lines are continuous and imaginary, though the field is real.