Electric Field Lines, Electric Dipoles

2. Electric Field Lines, Electric Dipoles Prepared By WaqasAmin Sheikh

3. Electric Field Lines • An electric field line is an imaginary line or curve drawn through a region of space so that its tangent at any point is in the direction of the electric field vector at that point

4. Electric Field Lines • Michael faraday first introduces the concept of field lines. He called them “lines of forces” but the term “field lines” is preferable • Electric field lines shows the direction of E at each point and their spacing gives a general idea of the magnitude of E at each point • Where E is strong we draw lines bunched closely together.

5. Electric Field Lines • Where E is weaker they are farther apart. • At any particular point the electric field has a unique direction • Only one field line can pass through each point of the field. • Field lines never intersect

6. Electric Field Lines • Fig. shows some of the electric field lines in a plane containing • Single +ve charge • Two equal magnitude charges(one +ve and one –ve) • Two equal -ve charge • These diagrams are called field maps

7. Electric Field Lines • The direction of the total electric field at every point in each diagram is along the tangent to the electric field line passing through the point • Arrowheads indicates the direction of the E field vector along each field line

8. Electric Field Lines • In the region where the field is larger such as between the +ve and –ve charges the field lines are drawn closer to eachother

9. Electric Field Lines • Where the field magnitude is small such as between the two -vecharges the lines are widely separated • In a uniform field the field lines are straight, parallel and uniformly spaced

10. Electric Dipole • The combination of two charges with equal magnitude and opposite sign are called an electric dipole

11. Electric Dipole • Fig. shows a molecule of water H 2O which in many ways behave like an electric dipole • The water molecule is electrically neutral but the chemical bonds within the molecule cause a displacement of charge • The result is a net –ve charge on the oxygen end of the molecule and a net +ve charge on the hydrogen end forming an electric dipole

12. Electric Dipole • Water is an excellent solvent for ionic substances such as table salt(NaCl) precisely because the water molecule is an electric dipole • When dissolved in water salt dissociates into a +ve sodium ion and a –ve chlorine ion. Which tend to be attracted to the –ve and +ve ends respectively of water molecule the holds the ions in solution

13. Electric Dipole • If water molecules were not electric dipoles water would be a poor solvent • What forces and torque does an electric dipole experience when placed in an external electric field ? • What electric field does an electric dipole itself produce?

14. What is torque • Torque is a measure of how much a force acting on an object causes that object to rotate

15. Electric Dipole • Let’s place an electric dipole in a uniform external electric field E as shown in fig. • The forces F+ and F- on the two charges both have magnitude qE but their direction are opposite and they add to zero

16. Electric Dipole • The net force on an electric dipole in a uniform external electric field is zero • However the two forces don’t act along the same line, so their torques don’t add to zero • We calculate torques with respect to the center of the dipole • Let the angle between the electric field E and the dipole axis be φ

17. Electric Dipole • Lever arm for the both F+ and F- is (d/2)sinφ • Torque of F+ and the torque F- both have the same magnitude of (qE)(d/2)sinφ, both torque tend to rotate the dipole clockwise. • Hence the magnitude of the net torque is juct twice the magnitude of either individual torque • τ= (qE)(d)sinφ

18. Electric Dipole • Where dsinφ is the perpendicular distance between the lines of action of the two forces . • The product of the charge q and the separation d is the magnitude of a quantity called the Electric dipole moment denoted by p • P =qd(magnitude of electric dipole moment)

19. Electric Dipole • The units of p are charge times distance(C.m) • We further define the electric dipole moment to be a vector quantity P with magnitude given by the equation and direction along the dipole axis from the –ve charge to the +ve charge • In terms of p for the magnitude τ of the torque exerted by the field becomes • τ= pEsinφ(magnitude of the torque on an electric dipole)

20. Electric Dipole • In term of vector form the dipole is given by • τ = p X E( torque on an electric dipole in vector form)

21. Potential energy of electric dipole • When a dipole changes direction in an electric field the electric torque does work on it. With a corresponding change in potential energy. • The work dw done by a torque t is given by

22. Potential energy of electric dipole