Which graphical representation of electric field of a

Which graphical representation of electric field of a point charge is correct? A B _ C D _ E) I do not know + +

A _ What if the magnitude of electric field exactly at the position of a point charge? Point charge does not exert field on itself!

The Superposition Principle The net electric field at a location in space is a vector sum of the individual electric fields contributed by all charged particles located elsewhere. The electric field contributed by a charged particle is unaffected by the presence of other charged particles.

The Superposition Principle If many more point charges are present (qi) we go for i and eventually for integral ! i

System consists of two point charges (+4) and (+1) +4 +1 How many points exist in space where E-field is equal zero? A) B) C) D) E) None One Two Infinite number I don’t know

E-field in the middle of uniformly positively charge ring is represented by y What is about any other point inside the ring? x A) B) C) D) Red arrow Blue arrow Zero I do not know

The E of a Uniformly Charged Sphere Can calculate using principle of superposition: for r>R (outside) for r<R (inside)

The Superposition Principle The electric field of a dipole: Electric dipole: Two equally but oppositely charged point-like objects s -q +q Example of electric dipole: HCl molecule What is the E field far from the dipole (r>s)?

Dipoles are ubiquitous 1. Atom will become dipole when it experiences electric field: 2. Some molecules exist in the form of permanent dipoles: HCl molecule

In Protein the carbonyl groups of polypeptides have substantial dipole moments and their electrostatic interactions make an important energetic contribution to the stability of an a-helix O C + D=3. 7 Debye

Calculating Electric Field Choice of the origin y s -q +q x z Choice of origin: use symmetry

1. E along the x-axis

Approximation: Far from the Dipole if r>>s, then While the electric field of a point charge is proportional to 1/r 2, the electric field created by several charges may have a different distance dependence.

2. E along the y-axis

2. E along the y-axis if r>>s, then at <0, r, 0>

3. E along the z-axis at <r, 0, 0> at <0, r, 0> or <0, 0, r> Due to the symmetry E along the z-axis must be the same as E along the y-axis!

Other Locations

The Electric Field Point Charge: + Dipole: for r>>s : y s -q z - at <r, 0, 0> at <0, r, 0> +q x at <0, 0, r>

System consists of two point charges (+1) and (-1) +1 -1 How many points exist in space where E-field is equal zero? A) B) C) D) E) None One Two Infinite number I don’t know

Dipole in a Uniform Field Forces on +q and –q have the same magnitude but opposite direction It would experience a torque about its center of mass. What is the equilibrium position? Electric dipole can be used to measure the direction of electric field.

Dipole Moment x: r>>s y, z: The electric field of a dipole is proportional to the Dipole moment: p = qs , direction from –q to +q Dipole moment is a vector pointing from negative to positive charge

Electric Field Electric field has units of Newton per Coulomb: [N/C]

A Fundamental Rationale • Convenience: know E at some location – know the electric force on any charge: • Can describe the electric properties of matter in terms of electric field – independent of how this field was produced. Example: if E>3 106 N/C air becomes conductor • Retardation Nothing can move faster than light c c = 300, 000 km/s = 30 cm/ns Coulomb’s law is not completely correct – it does not contain time t nor speed of light c. v<<c !!!

Example Problem y E=? A dipole is located at the origin, and is composed of particles with charges e and –e, separated by a distance 2 10 -10 m along the xaxis. Calculate the magnitude of the E field at <0, 2 10 -8, 0> m. Since r>>s: 200Å 2Å x Using exact solution:

Interaction of a Point Charge and a Dipole • Direction makes sense? - negative end of dipole is closer, so its net contribution is larger • What is the force exerted on the dipole by the point charge? - Newton’s third law: equal but opposite sign