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Electric Field

The area around a system of charges in which the effect of electric charge existing is called the electric field of that particular system of electric charges.

Let us consider F as total force acting on a charge q due to some system of charges.

F œ q
F/q = quantity obtained is independent of q = E

E depends on the magnitude of the electrical charges of the system, arrangement of electric charges and position vector of charge.

The force acting on a unit position charge at a given point in a system of charges is called the electric field or electric field intensity at that point.

When more than one electrical charge is present, the electric field is equal to the vector sum of all individual electric fields due to all the charges.

Electric field intensity = E = F/q = KQ / r2

Continuous distribution of charges:
Suppose we want to calculate the total electric force acting on any external charge q due to a continuous distribution of charge, then we have to imagine small elements of charge dq. The resultant force on q can then be calculated by taking vector sum of all the forces acting on charge q due to each of these small elements.

The continuous distributions of charges are three types:
  1. line distribution
  2. surface distribution
  3. volume distribution

Line distribution:
Here charge is distributed continuously over a line and is not uniform, so it will be different at different points on the line. It is called as linear charge density (λ). Line is divided into small segments of the length dl. The force acting on any electric charge q having position vector due to electric charge λ ( r ) | dl | present on the line is calculated and is integrated over the entire line distribution of charge

Surface distribution:
Charge is distributed continuously over a surface and surface charge density is σ (r), small segments of area da , then the force acting on any electric charge q having position vector due to electric charge σ (r) da present on the area element is calculated and is integrated over the entire surface.

Volume distribution:
Suppose electric charge is distributed continuously over some volume and the volume charge density is ρ (r), small segments of volume d v, then the force acting on any electric charge q having position vector due to electric charge ρ (r) dv  present on the volume element is calculated and is integrated over the entire volume.

Calculation:
Example-1: When an electron and proton both are present in an electronic field ……………..
a)  Only the magnitude of forces are same
b)  Acceleration produced in them are same
c)  Magnitude and acceleration produced in them are same.
d)  None of above.

Answer: When an electron and proton both are present in an electronic field only the magnitude of forces are same

Example-2: Match the following properties.
(A) (B)
Line charge density charge per unit volume of the line
Surface charge density Force acting on unit charge
Volume charge density charge per unit length of the line
Electric field intensity charge per unit surface of the line

(A) (B)
Line charge density charge per unit length of the line
Surface charge density charge per unit surface of the line
Volume charge density charge per unit volume of the line
Electric field intensity Force acting on unit charge

Example-3: An assembly is situated on X-axis, having the same magnitude of charges q at positions X=1, X=2, X=4, X=8 and so on. Calculate the electric field intensity arising due to the given assembly of charges at point X=0.
Reason:
Electric filed intensity: E = Kq / r2
E = Kq [1/12 + 1/22 + 1/42 + …] 
E = Kq [1 + 1/4 + 1/16 + …] applying mathematic formula S = a/1-r for infinite geometric series

E = Kq [1/(1-1/4)]
E = Kq [1/(4-1)]
E = 4Kq / 3


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