Electric Field and Electric Field Lines

Electric Field

    The place around a charge in which another charge experiences the force of attraction or repulsion is called Electric Field.

Intensity of Electric Field

    The force exerted on a unit positive charge placed at a point in the electric field is called the intensity of the electric field at that point, it is denoted by E.

`\star`    It is a vector quantity.

`\star`    Its unit is Newton per Coulomb and another unit of  Electric field is V/m.

`\star`    The dimensional formula is `[M^1L^1T^{-3}T^{-1}]`. 

    Mathematically, the intensity of the electric field is equal to the ratio of the force to the unit charge

`E = \frac{\vec F}{q_0}`

If the particle of charge q is placed in `\vec E` electric field intensity, then the force acting on charge q is

`\vec F = q \vec E`

Note -

 `\star`   If the particle is positively charged then the direction of force in the direction of the electric field and if the particle is negatively charged then the direction of force and direction of the electric field will be opposite.

 `\star`   If the charge is positive point charge then the electric field is radially outwards and if the charge is negative point charge then the electric field is radially inwards.

Electric Field Lines

Types of Electric Field

Uniform electric field

    If the intensity of the electric field is same at all points in the electric field, then it is called uniform electric field.

Non-uniform electric field

    If the intensity of the field is different at different points in the electric field, then it is called non-uniform electric field.

Variable electric field

    In an electric field, if the intensity of the electric field at any point varies continuously with time, then it is called a variable electric field.

Note -

`\star`    If electric field lines are straight, parallel, and at equal distance, then uniform field is generated there.

`\star`    If the lines of force are not present at straight, parallel, and equal distances, then an non-uniform electric field is generated there.

`\star`    The intensity of the electric field is high at that place where the electric field lines are close to each other.

`\star`    Where the electric field lines are far apart, the intensity of the electric field is less.

Electric Field Due to a Point Charge

    Suppose a +q charge is present at a point O, at r distance from it a point P is located, on which the test `q _0` is placed. The electric field is in the direction in which the force is exerted on the charge `q _0`.

Electric Field due to Point Charge

    

The force on positive test charge `q_0` at P due to charge +q , from Coulomb's law

`\vec F = \frac{K q q_0}{r^2} \hat r`

From definition

`\vec E = \frac{\vec F}{q_0} \hat r `

`\vec E = \frac{K q q_0}{q_0 r^2}\hat r`

`\vec E = \frac{K q }{ r^2}\hat r`

`\star`    The direction of electric field at point P will be towards `\vec{OP}`.

`\star`    It is clear that the electric field intensity is inversely proportional to the square of the distance. 

`\star`    The graph between electric field intensity and distance is -

The graph between electric field intensity and distance

`\star`    Electric field

`\vec E = \frac{K q }{ r^2}\hat r`

`\vec E = \frac{1}{4 \pi \epsilon_0} \frac{ q }{ r^2}\hat r`

If the point charge is placed in a medium of dielectric constant `\epsilon_r`. Then the electric field

` E = \frac{1}{4 \pi \epsilon_0 \epsilon_r} \frac{ q }{ r^2}\hat r`

` E = \frac{E}{\epsilon_r}`

    Thus, for a dielectric medium, the value of electric field intensity is `\epsilon_r` times less than that in vacuum.

Electric Field due to a System of Charges

    The electric field intensity at a point is equal to the vector sum of the intensities due to other charges around it.

    The electric field intensity at a point P is

`\vec E_p = \vec E_1 + \vec E_2 + ..............+ \vec E_n`

Here are

`\vec E_1 = \frac{K q_1}{r_1^2} \hat{r}_1`

`\vec E_2 = \frac{K q_2}{r_2^2} \hat{r}_2`

`\vec E_3 = \frac{K q_3}{r_3^2} \hat{r}_3`

..............................................

`\vec E_n = \frac{K q_n}{r_n^2} \hat{r}_n`

So, that 

`\vec E_p =``\frac{K q_1}{r_1^2} \hat{r}_1`+`\frac{K q_2}{r_2^2} \hat{r}_2`+`\frac{K q_3}{r_3^2} \hat{r}_3`+.......................+ `\frac{K q_n}{r_n^2} \hat{r}_n`

`\vec E_p =`K `[\frac{q_1}{r_1^2} \hat{r}_1`+`\frac{q_2}{r_2^2} \hat{r}_2`+`\frac{q_3}{r_3^2} \hat{r}_3`+.......................+ `\frac{q_n}{r_n^2} \hat{r}_n]`

`\vec E_p =``\frac{1}{4 \pi \epsilon_0}` `[\frac{q_1}{r_1^2} \hat{r}_1`+`\frac{q_2}{r_2^2} \hat{r}_2`+`\frac{q_3}{r_3^2} \hat{r}_3`+.......................+ `\frac{q_n}{r_n^2} \hat{r}_n]`

1. Q: What is the electric field due to a system of charges?

   A: According to the principle of superposition, the electric field intensity at a point is equal to the vector sum of the different intensities due to all the charges.

2. Q: How do you calculate the electric field due to a system of charges?

   A: According to the principle of superposition of charges, to find the electric field at a point, the electric fields generated due to all the charges are calculated and their vector sum is done. This vector sum is equal to the intensity of the electric field at that point.

3. Q: Can the electric field at a point be zero due to a system of charges?

   A: Yes, the electric field intensity due to a group of charges at a point can be zero, this happens when the vector sum of the intensities due to all the charges at that point is zero.

Electric Field Lines

Definition of Electric field lines

    The imaginary path of a unit positive charge in electric field is called electric field lines.

Properties of Electric Field Lines

`star`    The field lines never intersect each other, if they intersect each other than we fiend two directions of electric field which is not possible.

field lines never intersect

`star`    The field lines are perpendicular to the surface.

Electric Field Lines

`star`    The greater the magnitude of the charge, the greater the number of lines of force associated with it.

`star`    Electric field lines never forms closed loops.

`star`    Denser electric field lines represent strong electric field.

`star`    Electric lines of force start from a positive charge and end at a negative charge.

Electric Field Lines

`star`    Electric lines of force are in the form of open curves.

`star`    Electric lines of force repel each other.

`star`    Electric field lines is away from the positive electric charge.

`star`    Electric field lines is towards the negative electric charge.

`star`    The tangent drawn at any point on the electric field line shows the direction of the field at that point.

Direction of Electric Field

`star`    If the electric field lines are equally spaced, then they produce a uniform electric field.

Uniform electric field

`star`    The intensity of the electric field inside a conductor is zero, due to which electric field lines cannot exist inside the conductor or cannot pass through the conductor.

`star`    Electric field lines can be affected by the force of attraction between two objects that are oppositely charged. Due to this, they tend to contract in length.