Physics > Electrostatics > 10.0 Work done
Electrostatics
1.0 Introduction
2.0 Electric charge
3.0 Coulomb's law
3.1 Coulomb's law in vector relations
3.2 Comparision between coulomb's force and gravitational force
4.0 Principle of superposition
5.0 Continuous charge distribution
6.0 Electric field
6.1 Electric field due to a point charge
6.2 Electric field due to a ring of charge
6.3 Electric field due to a line of charge
7.0 Electric field lines
8.0 Insulators and conductors
9.0 Gauss's law
9.1 Electric field due to a point charge
9.2 Electric field due to a linear charge distribution
9.3 Electric field due to a plane sheet of charge
9.4 Electric field near a charged conducting surface
9.5 Electric field due to a charged spherical shell or solid conducting surface
9.6 Electric field due to a solid sphere of charge
10.0 Work done
10.1 Work done by electrical force
10.2 Work done by external force
10.3 Relation between work done by electrical & external force
11.0 Electric potential energy
12.0 Electric Potential
12.1 Properties
12.2 Use of Potential
12.3 Potential Due to Point Charge
12.4 Potential due to a Ring
12.5 Potential Due to Uniformly charged Disc
12.6 Potential Due To Uniformly Charged Spherical Shell
12.7 Potential Due to Uniformly Charged Solid Sphere
13.0 Electric dipole
13.1 Electric field due to a dipole at axial point
13.2 Electric field on equatorial line
13.3 Electric field at any point
13.4 Dipole in an external electric field
13.5 Potential due to an electric dipole
10.3 Relation between work done by electrical & external force
3.2 Comparision between coulomb's force and gravitational force
6.2 Electric field due to a ring of charge
6.3 Electric field due to a line of charge
9.2 Electric field due to a linear charge distribution
9.3 Electric field due to a plane sheet of charge
9.4 Electric field near a charged conducting surface
9.5 Electric field due to a charged spherical shell or solid conducting surface
9.6 Electric field due to a solid sphere of charge
10.2 Work done by external force
10.3 Relation between work done by electrical & external force
12.2 Use of Potential
12.3 Potential Due to Point Charge
12.4 Potential due to a Ring
12.5 Potential Due to Uniformly charged Disc
12.6 Potential Due To Uniformly Charged Spherical Shell
12.7 Potential Due to Uniformly Charged Solid Sphere
13.2 Electric field on equatorial line
13.3 Electric field at any point
13.4 Dipole in an external electric field
13.5 Potential due to an electric dipole
The relation between work done by electrical and external force is given by, $${W_{{\text{electrical force}}}} = - {W_{{\text{external force}}}}$$
From the table below we can easily understand the relation and difference between the two types of work done.
| Work done by electrical force | Work done by external force | |
| $${\left( {{W_{A \to B}}} \right)_{{\text{electrical force}}}} = \int {\overrightarrow F } .\,d\overrightarrow r $$$${\left( {{W_{A \to B}}} \right)_{{\text{electrical force}}}} = \int {Fdr\cos \left( {0^\circ } \right)} $$$${\left( {{W_{A \to B}}} \right)_{{\text{electrical force}}}} = F\int {dr} $$$${\left( {{W_{A \to B}}} \right)_{{\text{electrical force}}}} = Fd$$$${\left( {{W_{A \to B}}} \right)_{{\text{electrical force}}}} = qEd$$ | $${\left( {{W_{A \to B}}} \right)_{{\text{external force}}}} = - \int {\overrightarrow F } .\,d\overrightarrow r $$$${\left( {{W_{A \to B}}} \right)_{{\text{external force}}}} = - \int {Fdr\cos \left( {0^\circ } \right)} $$$${\left( {{W_{A \to B}}} \right)_{{\text{external force}}}} = - F\int {dr} $$$${\left( {{W_{A \to B}}} \right)_{{\text{electrical force}}}} = - Fd$$$${\left( {{W_{A \to B}}} \right)_{{\text{external force}}}} = - qEd$$ |
| $${\left( {{W_{A \to B}}} \right)_{{\text{electrical force}}}} = \int {\overrightarrow F } .\,d\overrightarrow r $$$${\left( {{W_{A \to B}}} \right)_{{\text{electrical force}}}} = \int {Fdr\cos \left( {180^\circ } \right)} $$$${\left( {{W_{A \to B}}} \right)_{{\text{electrical force}}}} = - F\int {dr} $$$${\left( {{W_{A \to B}}} \right)_{{\text{electrical force}}}} = - Fd$$$${\left( {{W_{A \to B}}} \right)_{{\text{electrical force}}}} = - qEd$$ | $${\left( {{W_{A \to B}}} \right)_{{\text{external force}}}} = - \int {\overrightarrow F } .\,d\overrightarrow r $$$${\left( {{W_{A \to B}}} \right)_{{\text{external force}}}} = - \int {Fdr\cos \left( {180^\circ } \right)} $$$${\left( {{W_{A \to B}}} \right)_{{\text{external force}}}} = F\int {dr} $$$${\left( {{W_{A \to B}}} \right)_{{\text{electrical force}}}} = Fd$$$${\left( {{W_{A \to B}}} \right)_{{\text{external force}}}} = qEd$$ |
