dipoleElectrostatic Energy ErSomesh Kumar Malhotra Assistant Professor ECE Department UIET Electric Dipole An electric dipole is formed when two poim charges of equal magnitude but opposite sign are separated by a small distance ID: 1022105
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1. Electrostatic IV(Electric dipole,Electrostatic Energy)Er.Somesh Kumar MalhotraAssistant ProfessorECE Department, UIET
2. Electric DipoleAn electric dipole is formed when two poim charges of equal magnitude but opposite sign are separated by a small distance.Consider the dipole shown in Figure. The potential at point P is given by
3. Electric Dipole
4. Electric DipoleElectric field due to dipole with centre at the origin
5. Example 1
6. ENERGY DENSITY IN ELECTROSTATIC FIELDSTo determine the energy present in an assembly of charges, we must first determine the amount of work necessary to assemble them. Suppose we wish to position three point charges Q1, Q2, and Q3 in an initially empty space shown shaded in Figure. No work is required to transfer Q1 from infinity to P1 because the space is initially charge free and there is no electric field The work done in transferring Q2 from infinity to P2 is equal to the product of Q2 and the potential V21 a t P2 due to Q1. Similarly, the work done in positioning Q3 at P3 is equal to Q3(V32 + V31), where V32 and V31 are the potentials at P3 due to Q2 and Q1 respectively. Hence the total work done in positioning the three charges is
7. ENERGY DENSITY IN ELECTROSTATIC FIELDS
8. ENERGY DENSITY IN ELECTROSTATIC FIELDS
9. ENERGY DENSITY IN ELECTROSTATIC FIELDSwe recall that V varies as 1/r and D as 1/r2 for point charges; V varies as 1/r2 and D as 1/r3 for dipoles; and so on. Hence, VD in the first term on the right-hand side of eq. must vary at least as 1/r3 while dS varies as r2. Consequently, the first integral in eq. must tend to zero as the surface S becomes large.
10. ENERGY DENSITY IN ELECTROSTATIC FIELDS
11. Example 2
12. Example 3
13. Example 3