# Is Electric Field A Vector? 5 Facts You Should Know

The electric field is generated due to the charged particle. This article will elucidate whether the electric field is a scalar or a vector quantity.

The electric field is a vector as it has a direction and lies along the direction of the electric force felt on the charges in a field. The electric field is a vector mainly because of the electric force quantity. The direction of the electric field is determined by the charge on the particle/ surface.

The direction of the electric field from the positive charge is directed outward, and that of the negative charge is inward. We shall further see in this article how to determine the direction and magnitude of the electric field and different facts about the electric vector field.

## Why is electric field a vector quantity?

The vector quantities have a particular direction along with the magnitude. Let us clarify what makes the electric field a vector quantity.

The electric field is a vector quantity because it has a direction based on the particle’s charge. The electric field is a ratio of electric force and charge. The charge is a scalar quantity, but the electric force is a vector quantity, and therefore the electric field has magnitude and direction both.

## How is electric field a vector quantity?

The electric field is present all around the electric field region surrounding the charge. Let us see how the electric field has a direction throughout the region.

The electric field is a vector quantity based on the fact that the electric flux running through the field exerts an electric force on the particle, which is a vector quantity. The electric field lines run through the field, denoting the direction of the electric field.

## What is the direction of electric field?

The direction of the electric field shows the orientation of a field. Let us discuss the direction of the electric field in detail and see how it relates to the charge and force.

The electric field lines run from a positive to a negative charge, and their direction is parallel to the electric force exerted on the charges. The direction of the electric field is established by the particle’s charge and is the same throughout the electric field region.

## How to calculate the magnitude of electric field?

The electric field depends upon the charge and the distance between the point of consideration to the charge. Let us see how to calculate the magnitude of the electric field.

The formula used to calculate the magnitude of the electric field is E = klQl/r2, where E is the electric field, k is the electric field constant (9×109 Nm2/C2), lQl is a magnitude of charge, and r is a distance between the charge and a point. It is related to the magnitude of charge, hence always positive.

An electric field magnitude can also be calculated as the ratio of potential difference and distance between the charge and point. The magnitude of the electric field is constant if the potential difference between any two points is the same and is valid for the uniform electric field.

### What is the magnitude of the electric field at a point due to charges +3 C and -2 C located at a distance of 3 m and 4 m away from a point?

Given: The charge q = +3 C.

The second charge Q = -2 C.

The distance between the charge q and a point is a = 3 m.

The distance between the charge Q and a point is b = 4 m.

The formula used to calculate the magnitude of the electric field is,

lEl = klQl/r2

The net magnitude of the electric field at a point due to both the charges is,

lEl = lE1l+ lE2l

Here, lE1l is the magnitude of an electric field at a point due to charge q, and lE2l is the magnitude of an electric field at a point due to charge Q.

Using the formula in the above expression, we get,

lEl = klql/a2 + klQl/b2 = k(lql/a2 + lQl/b2)

Substituting values in the above equation, we get,

lEl = 9×109 Nm2/C2 {(l+3 Cl/(3 m)2)+ (l-2 Cl/(4 m)2)}

lEl = 9×109 Nm2/C2 {(3 C/9 m2) + (2 C/16 m2)}

lEl = 9×109 Nm2/C2 ×1C/m2 ×(1/3+ 1/8}

lEl = 9×109 × 0.45 N/C

lEl = 4.05×109 N/C

Hence, the magnitude of the electric field at a point due to both the charges is 4.05×109 N/C.

## Why electric field lines are vector quantities?

The electric field lines are the electric flux running through the electric field region, which has a direction. Let us discuss why these field lines are vector in nature.

The electric field lines are vector quantities because they have direction and magnitude. The electric field lines arise from the positive charge and wind up to the negative charge. The direction of the electric force is in the direction of the electric field lines.

#### Conclusion

We can conclude with this article that the electric field is a vector quantity due to the electric field lines originating from the positive charge and terminating at the negative. The electric field direction is parallel to the electric force. It has a scalar quantity due to its charge and a vector due to the force.