# Electric Field

## Electric Field

Let us see, what is field? Consider a magnet. it has its own effect in a
region surrounding it. The effect can be experienced by placing another
magnet near the first magnet. Such an effect can be defined by a
particular physical function. In the region surrounding the magnet,
there exists a particular value for that physical function, at every
point, describing the effect of magnet.

So Field can be defined as the region in which, at each point there exists a corresponding value of some physical function.

Let us study What is this

We know that there are generally two types of charges existing in nature:

To generalize the definition of electric field considers that a very small test charge q

Electric field or the strength of the electric field produced by the object having charge Q

|E| = So Field can be defined as the region in which, at each point there exists a corresponding value of some physical function.

Let us study What is this

**Electric Field**?We know that there are generally two types of charges existing in nature:

- Positive
- Negative.

To generalize the definition of electric field considers that a very small test charge q

_{0}is placed near to the object carrying much higher positive charge having value Q_{0}.Electric field or the strength of the electric field produced by the object having charge Q

_{0}on the positive test charge q_{0}is defined as the Electric force per unit charge.
Where F

q

Thus Electric field

_{e}= Force due to the charge q_{o }q

_{0}= Test Charge coming in the electric field.Thus Electric field

**E**is defined as ratio of the electric force acting on the positive test charge q_{0}and divided by the magnitude of the positive test charge.## Electric Field Equation

_{0}and divided by the magnitude of the positive test charge.The Electric field formula is given by:

|E| =

**|E|**is the

**Magnitude of Electric Field**is considered,

**F**is the electric force acting on the positive test charge

_{e}**,**

qis the positive test charge.

q

_{0}Note that electric field considered above is produced by the charge which is external to the test charge q

_{0}and not by the positive charge itself.

Electric field is the property of the source for example every electron come within its electric field.

The above formula is used in

**Calculating Electric Field**at a point.

## Electric Field Units

|E| =

**Newton**and SI unit of the charge is

**Coulomb**.

Unit of electric field will be

**N/C**.

## Electric Field Direction

To
determine the direction of the electric field consider that charge

**Q**and**q**i.e. positive test charge are present. Now the electric force between the charge_{0}**Q**and the**q**is given by the Coulomb force._{0}**Q**and

**q**is given by the formula as

_{0}
F = ke(|Q||q0|)r^d2 .Where

And

According to the electric field formula

E = **F**= Electrostatic force between two charges**d**= distance between Q and q_{0}**Q, q**= Electrostatic charges._{0}**k**= Coulomb constant._{e}And

**is the unit vector directed from the charge**r^ **Q**towards the test charge**q**._{0}According to the electric field formula

_{e}, we get

E =

Thus Electric Field formula is given by

E =

Here
E is also termed as the

The

**Electric Field Intensity**. Note that the electric field is a vector quantity as it has both magnitude and the direction associated with it.The

**Electric Field Strength**produced by charge**Q**is given by
E = ke(|Q|)r^d2 . Therefore the
direction of the electric field produced by the charge

**Q**is radially outward if the charge**Q**is positive and the electric field produced by the electric charge**Q**is radially inward if the charge**Q**is negative.## Electric Field Lines

**Electric Field Lines**are produced by the negative charge as shown in the figure below.

They are nothing but a way of pictorially mapping the electric field around a configuration of charges. It is the curve drawn in such a way that the tangent to it at each point is in the direction of the net field at the point. An arrow on the lines of force is a must to indicate the direction of the electric field.

In space, electric field is produced by the charges. Electric
field lines are drawn to signify the direction of the electric field and
the strength of the electric field at various points in space.

## Electric Field Potential

Electric potential at a point
is defined as the amount of work done in bringing unit positive charge
from infinity to that point. Electric potential is a scalar quantity.

Electric field potential or

Electric field potential or

**Electric Field Voltage**at a point is equal to the electric potential energy of a charged particle at that location divided by the charge particle.**P**due to charge

**Q**is given by

V =

r is the distance between the charges

it is also termed as the

**Electric Potential**or the

**Electrostatic Potential**. The Unit of electric field potential is

**Joules per Coulomb**.

## Dipole Electric Field

**P**.

**P**is equal to the product of the charge

**q**present in the dipole and the distance

**d**between the two charges of the dipole.

The Formula for Electric dipole moment is given by

E=

**|qd|**Where

**P**is a vector quantity.

Direction of the electric dipole moment is from the negative charge to the positive charge present in the dipole. The field which is produced inside the dipole is given in the figure below.

In the figure shown below note that the electric field is shown in direction radially outward from the positive charge of the dipole and radially inward in case of the negative charge of the dipole.

E =

## Electric Field inside a Sphere

Hence we have

*da*is area of the sphere and the total charge enclosed is given by the sum of the point charge and the product of the volume of the sphere and the charge density and hence

E(4

^{2}) =

E =

**E**is the electric field inside the sphere

**Q**is the net charge on the sphere

**r**is the radius of the sphere.

## Electric Field of a Wire

## Electric Field Capacitor

= 8.854

^{-12}F/m.

Where charge density
is defined as the ratio of the charge per unit area.

This is the net electric field produced inside the capacitor charged plates.

This is the net electric field produced inside the capacitor charged plates.

## Net Electric Field

The Net electric field is
defined as the total field experienced by a point under the various
charges in the system. To understand it better we will look at the
problems below.

Let us consider the following charges q

Let us consider the following charges q

_{1}, q_{2}, q_{3}, ............. q_{n}.q = q

_{1}+ q

_{2}+ q

_{3}+ q

_{4}+ ...... +q

_{n.}

## Uniform Electric Field

The uniform electric field is the electric field which is not changing with respect to time. It is constant and not varying.Consider the parallel plate capacitor, we could see the electric field is same at all point from positive end to the negative end.

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