**Electric Field**

An electric field is a vector field that describes the force exerted by a charged object on other charged objects in its vicinity. It is a fundamental concept in electromagnetism and is essential for understanding the behavior of electrically charged particles and systems.

The electric field at a given point in space is defined as the force per unit charge that would be exerted on a small test charge placed at that point. Mathematically, the electric field is given by:

E = F / q

where E is the electric field, F is the force exerted on the test charge, and q is the magnitude of the test charge. The direction of the electric field is defined as the direction in which a positive test charge would be pushed or pulled if placed at that point in space.

The electric field is a vector field, meaning that it has both magnitude and direction at every point in space. The magnitude of the electric field is directly proportional to the magnitude of the source charge and inversely proportional to the distance from the source charge.

Mathematically, the electric field due to a point charge q at a distance r is given by Coulomb’s law:

E = kq / r^{2}

where k is Coulomb’s constant, with a value of approximately 9 × 10^{9} N·m^{2}/C^{2}.

The electric field can also be described in terms of **electric field lines**. Electric field lines are imaginary lines that are drawn in a way that the direction of the electric field at any point is tangent to the line at that point. **The density of electric field lines is proportional to the magnitude of the electric field**, and the lines never cross each other. Electric field lines provide a graphical representation of the electric field and are useful for visualizing the behavior of electrically charged systems.

## Numerical Problems Based on Electric Field for Class 12 Physics

Here we are providing numerical problems based on Electric Field for Class 12 Physics.

Q.1. If an oil drop of weight 3.2 × 10^{-13} N is balanced in an electric field of 5 × 10^{3} Vm^{-1}, find the charge on the oil drop.

(Ans. 0.64 × 10^{-18} C)

Q.2. A charged oil drop remains stationary when situated between two parallel plates 20 mm apart and a p.d. of 500 V is applied to the plates. Find the charge on the drop if it has a mass of 2 × 10^{-4} kg. Take g – 10 ms^{-2}.

(Ans. 8 × 10 ^{-13} C)

Q.3. A particle of mass 10^{-3} kg and charge 5 μC is thrown at a speed of 20 ms^{-1} against a uniform electric field of strength 2 × 10^{5} NC^{-1}. How much distance will it travel before coming to rest momentarily?

(Ans. 0.2 m)

Q.4. Calculate the magnitude of the electric field, which can just balance a deuteron of mass 3.2 × 10^{-27} kg. Take g = 10 ms^{-2}.

(Ans. 2.0 × 10^{– 7} NC^{-1})