1. Chapter 22 Gauss’s Law

2. Charles Allison © 2000 21-10 Motion of a Charged Particle in an Electric Field The force on an object of charge q in an electric field is given by: = q Therefore, if we know the mass and charge of a particle, we can describe its subsequent motion in an electric field.

3. Charles Allison © 2000 21-10 Motion of a Charged Particle in an Electric Field Example 21-15: Electron accelerated by electric field. An electron (mass m = 9.11 x 10 -31 kg) is accelerated in the uniform field (E = 2.0 x 10 4 N/C) between two parallel charged plates. The separation of the plates is 1.5 cm. The electron is accelerated from rest near the negative plate and passes through a tiny hole in the positive plate. (a) With what speed does it leave the hole? (b) Show that the gravitational force can be ignored. Assume the hole is so small that it does not affect the uniform field between the plates.

4. Charles Allison © 2000 21-11 Electric Dipoles An electric dipole consists of two charges Q, equal in magnitude and opposite in sign, separated by a distance.The dipole moment, p= Q, points from the negative to the positive charge.

5. Charles Allison © 2000 21-11 Electric Dipoles An electric dipole in a uniform electric field will experience no net force, but it will, in general, experience a torque:

6. Charles Allison © 2000 21-11 Electric Dipoles The electric field created by a dipole is the sum of the fields created by the two charges; far from the dipole, the field shows a 1/r 3 dependence :

7. Charles Allison © 2000 Electric flux: Electric flux through an area is proportional to the total number of field lines crossing the area. 22-1 Electric Flux

8. Charles Allison © 2000 22-1 Electric Flux Example 22-1: Electric flux. Calculate the electric flux through the rectangle shown. The rectangle is 10 cm by 20 cm, the electric field is uniform at 200 N/C, and the angle θ is 30°.

9. Charles Allison © 2000 Flux through a closed surface: 22-1 Electric Flux E leaving the surface θ< π/2 E entering the surface θ> π/2 So the net flux out of the volume is 0 If the flux is negative there is no net flux into the volume

10. Charles Allison © 2000 The net number of field lines through the surface is proportional to the charge enclosed, and also to the flux, giving Gauss’s law: This can be used to find the electric field in situations with a high degree of symmetry. 22-2 Gauss’s Law

11. Charles Allison © 2000 22-2 Gauss’s Law For a point charge, Therefore, Solving for E gives the result we expect from Coulomb’s law: