Question

State the principle of superposition of charges. Derive an expression for the force on a charge "q" due to discrete position of n-charges in terms of their position vectors.​

Answer 1

HEAR THIS MARK ME AS THE BRAINLIEST

Answer:

Electric field due to a system of point charges.

Consider a system of N point charges q

1

,q

2

,...q

N

, having position vectors

r

1

,

r

2

,...,

r

N

with respect to origin O. We wish to determine the electric field at point P whose position vector is

r

.

According to Coulomb's law, the force on charge q

0

due to charge q

1

is

F

1

=

4πϵ

0

1

⋅

r

2p

2

q

1

q

0

r

^

1P

Where

r

^

1P is a unit vector in the direction from q

1

to P and r1p is the distance between q

1

and P.

Hence the electric field at point P due to charge q

1

is

E

1

=

q

0

F

1

=

r

1P

2

1

r

^

1P

Similarly, electric field at P due to charge q

2

is

E

2

=

4πϵ

0

1

⋅

r

2P

2

q

2

r

^

2P

According to the principle of superposition of electric fields, the electric field at any point due to a group of point charges is equal to the vector sum of the electric fields produced by each charge individually at that point, when all other charges are assumed to be absent.

Hence, the electric field at point P due to the system of N charges is

Answer 2

The principle of superposition of charges can be stated as follows.

"If a system contains a number of interacting charges then the net force on any one charge due to the other charges is the vector sum of all the forces exerted on it by all the other charges."

The individual forces are not affected by the presence of the other charges. So, the force that two charges exert on each other is not changed by the presence of other charges.

If the distance between the charges q₁ and q₂ is r₁₂, then the force on q₁ due to q₂ is given by the following formula.

        $\vec F_{12} = \frac{1}{4\pi \epsilon _{0}} \frac{q_{1} q_{2}}{r_{12} ^{2}}$

Similarly, the forces on a charge q₁ due to discrete position of n-charges in terms of their position vectors are given by

        $\vec F_{1n} = \frac{1}{4\pi \epsilon _{0}} \frac{q_{1} q_{n}}{r_{1n} ^{2}}$