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# Conservative Electrostatic Forces Assignment Help

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Electrostatics - Conservative Electrostatic Forces

**Conservative Electrostatic Forces**

To prove that electrostatic forces are conservative in nature, we show that work done in moving a unit positive test charge over a closed path in an electric field is zero. We know that along any path L work done in carrying unit positive charge from A to B.

W_{AB}/q_{0} = V_{B} – V_{A}

Similarly work done in carrying unit positive charge from B to A along another path L’

**W **_{BA} / q_{0} = V_{A} – V_{B}

Adding the two we het

**W**_{AB}/ q_{0} + W_{BA}/ q_{0} = W_{AB}A/ q_{0} = (V_{B} – V_{A}) + (V_{A} – V_{B}) = Zero

Hence no work is done is moving a unit positive test charge over a closed path in an electric field. Hence electrostatic field is a conservative filed and electrostatic forces are conservative forces in nature.

Mathematically we can write this result as

ƒ~E. ~dl = 0

Line integral of electric field over a closed path in the electric fields is always zero.

Electric potential due to a point charge

Suppose we have to calculate electric potential at any point p due to single point charge **+ q at O; where OP = r **

By definition, electric potential at p is the amount of work done in carrying a unit positive charge form ∞ to p.

As work done is independent of the path, we choose a convenient path along the radial direction from infinity to the point P.

At some intermediate point A on this path, where OA = x, the electrostatic force on unit positive charge is

**E = 1 4π∈**_{0} x^{2} along OA produced

Small amount of work done in moving a unit positive charge from A to B where **AB = dx** is

**dW = E, dx = E dx cos 180 = - E dx **

Total work done in moving unit + charge from ∞ to the point p is

**W = ∫**_{∞}^{r}-E dx =∫_{∞}^{r}- 1 4π ∈_{0} q / x2 dx = - q / 4π∈_{0} ∫x ^{– 2} dx = - q / 4π∈_{0} [- 1 / x] r

Conservative Electrostatic Forces Assignment Help, Conservative Electrostatic Forces Homework Help, Conservative Electrostatic Forces Tutors, Conservative Electrostatic Forces Solutions, Conservative Electrostatic Forces Tutors, Electrostatics Help, Physics Tutors, Conservative Electrostatic Forces Questions Answers

**Conservative Electrostatic Forces**

W

W

_{AB}/q_{0}= V_{B}– V_{A}Similarly work done in carrying unit positive charge from B to A along another path L’

**W**

_{BA}/ q_{0}= V_{A}– V_{B}

Adding the two we het

**W**

_{AB}/ q_{0}+ W_{BA}/ q_{0}= W_{AB}A/ q_{0}= (V_{B}– V_{A}) + (V_{A}– V_{B}) = ZeroHence no work is done is moving a unit positive test charge over a closed path in an electric field. Hence electrostatic field is a conservative filed and electrostatic forces are conservative forces in nature.

Mathematically we can write this result as

Line integral of electric field over a closed path in the electric fields is always zero.

Electric potential due to a point charge

Suppose we have to calculate electric potential at any point p due to single point charge

**+ q at O; where OP = r**

By definition, electric potential at p is the amount of work done in carrying a unit positive charge form ∞ to p.

As work done is independent of the path, we choose a convenient path along the radial direction from infinity to the point P.

At some intermediate point A on this path, where OA = x, the electrostatic force on unit positive charge is

**E = 1 4π∈**along OA produced

_{0}x^{2}Small amount of work done in moving a unit positive charge from A to B where

**AB = dx**is

**dW = E, dx = E dx cos 180 = - E dx**

Total work done in moving unit + charge from ∞ to the point p is

**W = ∫**

_{∞}^{r}-E dx =∫_{∞}^{r}- 1 4π ∈_{0}q / x2 dx = - q / 4π∈_{0}∫x^{– 2}dx = - q / 4π∈_{0}[- 1 / x] r