Revision: Electrostatics JEE Main Electrostatics

A time-dependent combination of electric and magnetic fields that propagates through space and can transport energy is called an electromagnetic field.

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.

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

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 phenomenon in which the electric field inside a cavity of a conductor is zero, irrespective of external charges or fields, is called electrostatic shielding.

The ratio of the permittivity of a medium to the permittivity of vacuum.

K = ε / ε₀

OR

Dielectric constant is the factor by which the capacitance of a capacitor increases when a dielectric is completely inserted between its plates.

The product of vacuum permittivity and dielectric constant of the medium.

ε = ε₀K

\[\vec τ\] = \[\vec p\] × \[\vec E\]

Magnitude: τ = pE sin θ

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

\[\vec{E}=\frac{\sigma}{\varepsilon_0}\hat{n}\]

where
σ = surface charge density
\[\hat n\] = outward normal unit vector

Magnitude form:

E = \[\frac{\sigma}{\varepsilon_0}\]

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)`

• The electric field due to many charges is the force on a unit test charge at that point.
• The total electric field is the vector sum of fields due to each charge (superposition principle).
• The electric field depends on the positions of the charges and changes from point to point in space.

• An electric field describes the electrical effect of a system of charges and does not depend on the test charge used to measure it.
• It is a vector quantity defined at every point in space and can vary from point to point.
• In changing situations, electromagnetic fields travel at the speed of light and can carry energy from one place to another.