Forces and fields obey the superposition principle Field

Forces and fields obey the superposition principle: Field from a group of particles is a vector sum of fields from each particle

Electric Field Properties • A small positive test charge is used to determine the electric field at a given point • The electric field is a vector field that can be symbolized by lines in space called electric field lines • The electric field is continuous, existing at every point, it just changes in magnitude with distance from the source

Electric Field Equation • Electric Field • For a continuous charge distribution

For spatially distributed charges – we can sub-divide the object into the small, “point-like” charges and integrate (sum up) the individual fields. Often, we assign charge density for such spacious charged objects

Examples of field calculations: fields of continuous charge distributions Field of a ring of charge on the symmetry axis

Positive charge is uniformly distributed around a semicircle. The electric field that this charge produces at the center of curvature P is in A. the +x-direction. B. the –x-direction. C. the +y-direction. D. the –y-direction. E. none of the above

Field of a disk, uniformly charged on the symmetry axis Surface charge density is s, radius R Area d. A of a ring of radius r Changing variable of integration For the limit of x<<R, we have an electric field of the infinite plane sheet of charge and it is independent of the distance from the plane (assuming that distance x<<linear dimensions of the sheet)

Electric Field Line Properties • Relation between field lines and electric field vectors: a. The direction of the tangent to a field line is the direction of the electric field E at that point b. The number of field lines per unit area is proportional to the magnitude of E: the more field lines the stronger E • Electric field lines point in direction of force on a positive test charge therefore away from a positive charge and toward a negative charge • Electric field lines begin on positive charges and end on negative charges or infinity • No two electric field lines can cross

Electric field lines E is tangent to the electric field line – no 2 lines can cross (E is unique at each point) Magnitude of E is proportional to the density of the lines

Remember, electric field lines are NOT trajectories! When a particle moves on a curved path, the direction of acceleration (and hence of the force) is not collinear with the tangent to the curve

Electric dipole Many physical systems are described as electric dipoles – hugely important concept Water is a good solvent for ionic and polar substances specifically because of its dipole properties

Torque on the electric dipole (electric dipole moment from “-” to “+”) Electric field is uniform in space Net Force is zero Net Torque is not zero (torque is a vector) Stable and unstable equilibrium

Charge #2 Three point charges lie at the vertices of an equilateral triangle as shown. Charges #2 and #3 make up an electric dipole. The net electric torque that Charge #1 exerts on the dipole is +q Charge #1 +q y –q x A. clockwise. B. counterclockwise. C. zero. D. not enough information given to decide Charge #3

Electric field of a dipole E-field on the line connecting two charges - A + d when r>>d E-field on the line perpendicular to the dipole’s axis A d + General case – combination of the above two

Dipole’s Potential Energy E-field does work on the dipole – changes its potential energy Work done by the field (remember your mechanics class? ) Dipole aligns itself to minimize its potential energy in the external E-field. Net force is not necessarily zero in the non-uniform electric field – induced polarization and electrostatic forces on the uncharged bodies

Reading Assignment : Chapter 21. 5 - 21. 7 Next Lecture – in-class quiz about the material we covered (chapter 21 ) Homework Assignment: Check www. masteringphysics. com this afternoon Due next Tuesday by end of class