Scalar field: Temperatures The shown temperatures are samples of the field

Vector field: Winds

3. Electric field Coulomb’s low and electric field Q q - test charge Definition Units (Action at a distance?) If the electric force on a test charge q located at point P is F, then the electric field at point P is F/q. Because the force is always proportional to q, the electric field is independent of the test charge! P Charge Q creates an electric (electrostatic) field E. Charge q is used to find this electric field E.

Example: A negative charge, placed in the electric field between two charged plates, experiences an electric force as shown below. What is the direction of the electric field? A. LeftB. Right C. Upward D. Downward The negative charge is attracted by the positive plate and is repelled from the negative plate The electric field is directed from the positive to the negative charge! Example: Between the red and the blue charges, which of them experiences the greater electric field due to the green charge? dd same electric field same point in space Both charges feel the same electric field due to the green charge because they are at the same point in space!

Example (Electron in a uniform electric field): Describe the motion of an electron that enters a region with a uniform electric field having initial velocity perpendicular to the direction of the field Once the electric field is known, finding the force on a given charge is simple… Constant acceleration in the –y direction. Identical to projectile motion! F = –|q e |E parabola E v0v0 electron

Two most important questions: 1)How can one find force, F on the electric charge, q, exerted by field E? 2)How can electrostatic field E be created? Answers: 1) 2) Field E is due to other charges 2a) Field due to a single charge: 2b) Field due to a number of charges: Principle of superposition has been used in 2b)

Q1Q1 Q3Q3 Q4Q4 Q7Q7 Q2Q2 Q6Q6 Q5Q5 Q8Q8 q1q1 Charges Q 1, Q 2 … create electric field. This field is independent from the test charge q 1. If we will replace the charge q 1 with another charge q 2, then the force on the new charge will be different then, but the electric field is independent from q. test charge These charges create electric field Definition of electric field Principle of superposition

Example (Net electric field ): Which of the three vectors best represents the direction of the net electric field at the location of charge Q? Q q 1 < 0 q 2 > 0 C A B E1E1 E2E2 E net Example: Calculate the electric field at the center of a square 52.5 cm on a side if one corner is occupied by a charge +45μC and the other three are occupied by charges -27μC.

Electric field lines Definition: Electric field lines indicate the direction of the force due to the given field on a positive charge, i.e. electric force on a positive charge is tangent to these lines Number of these lines is proportional to the magnitude of the charge Properties: Electric field lines start on positive charges or came from infinity, they end on negative charges or end at infinity Density of these lines is proportional to the magnitude of the field +Q -Q - -2Q

Electric Field Lines Around Electric Charges A single positive charge (an electric monopole) A positive charge and a negative of equal magnitude (an electric dipole) Two equal positive charges

Example: A. E 1 = E 2 > E 3 B. E 1 > E 2 > E 3 C. E 1 > E 2 ; E 3 = 0 The electric field lines in a certain region of space are as shown below. Compare the magnitude of the electric field at points 1, 2 and 3. The magnitude of the electric field is proportional to the local density of lines. Being on the same line or being between the lines is totally irrelevant.

Electric field in conductors The electric field inside a conductor in equilibrium is always zero. The electric field right outside a conductor in equilibrium is perpendicular to the surface of the conductor. We cannot have a force parallel to the surface (would produce motion), but perpendicular to it is OK. E = 0

Example: A 4.7μC and a -3.5μC charge are placed 18.5 cm apart. Where can a third charge be placed so that it experiences no net force? x – d To experience no net force, the third charge Q must be closer to the smaller magnitude charge (the negative charge). The third charge cannot be between the charges, because it would experience a force from each charge in the same direction, and so the net force could not be zero. And the third charge must be on the line joining the other two charges, so that the two forces on the third charge are along the same line. Equate the magnitudes of the two forces on the third charge, and solve for x > 0.