Electric Fields, Voltage, Electric Current, and Ohm’s Law

Electric Fields, Voltage, Electric Current, and Ohm’s Law ISAT 241 Fall 2003 David J. Lawrence

Properties of Electric Charges • Twokinds of charges. Unlike charges attract, while like charges repel each other. • The force between charges varies as the inversesquare of their separation: F µ 1/r2. • Charge is conserved. It is neither created nor destroyed, but is transferred. • Charge is quantized. It exists in discrete “packets”: q = +/- N e, where N is some integer.

Serway & Jewett, Principles of Physics, 3rd ed. Figure 19.2

Properties of Electric Charges • “Electric charge is conserved” means that objects become “charged” when charges (usually electrons) move from one neutral object to another. • This movement results in • a Net Positivecharge on one object, and • a Net Negativecharge on the other object.

Properties of Electric Charges • Neutral, uncharged matter contains as many positive charges as negative charges. • Net charge is caused by an excess (or shortage) of charged particles of one sign. • These particles are protons and electrons.

Properties of Electric Charges • Charge of an electron = -e = -1.6 ´ 10-19 C • Charge of a proton = +e = +1.6 ´ 10-19 C • “C” is the Coulomb. • Charge is Quantized! • Total Charge = N ´ e = N´ 1.6 ´ 10-19 C where N is the number of positive charges minus the number of negative charges. • But, for large enough N, quantization is not evident.

Electrical Properties of Materials • Conductors: materials in which electric charges move freely, e.g., metals. • Insulators: materials that do not readily transport charge, e.g., most plastics, glasses, and ceramics.

Electrical Properties of Materials • Semiconductors: have properties somewhere between those of insulators and conductors, e.g., silicon, germanium, gallium arsenide, zinc oxide. • Superconductors: “perfect” conductors in which there is no “resistance” to the movement of charge, e.g., some metals and ceramics at low temperatures: tin, indium, YBa2Cu3O7

Coulomb’s Law • The electric force between two charges is given by: (newtons, N) • Attractive if q1 and q2 have opposite sign. • Repulsive if q1 and q2 have same sign. • r = separation between the two charged particles. • ke = 9.0 x 109 Nm2/C2 = Coulomb Constant.

Coulomb’s Law • Force is avector quantity. =electric force exerted by q1 on q2 • r12 = unit vector directed from q1 to q2 Ù

y mo g Gravitational Field • Consider the uniform gravitational field near the surface of the earth • If we have a = small “test mass” mo , the force on that mass is Fg = mo g • We define the gravitational field to be Recallthat g = | g | = 9.8 m/s2

q FE q >> qo qo The Electric Field • The electric field vector E at a point in space is defined as the electric force FE acting on a positive “Test Charge” placed at that point, divided by the magnitude of the test charge qo.

q FE q >> qo qo The Electric Field • Units: • ~newtons/coulomb, N/C

Serway & Jewett, Principles of Physics, 3rd ed. See Figure 19.11

E - + FE FE The Electric Field • In general, the electric force on a charge qo in an electric field E is given by

The Electric Field • E is the electric field produced by q, not the field produced by qo. • Direction of E = direction of FE (qo > 0). • qo << |q| • We say that an electric field exists at some point if a test charge placed there experiences an electric force.

q q qo E E qo |q| >> qo q >> qo The Electric Field • For this situation, Coulomb’s law gives: FE = |FE| = ke (|q||qo|/r2) • Therefore, the electric field at the position of qo due to the charge q is given by: E = |E| = |FE|/qo = ke (|q|/r2)

y mo g Gravitational Field Lines • Consider the uniform gravitational field near the surface of the earth = g • If we have a small “test mass” mo , the force on that mass is Fg = mo g • We can use gravitational field lines as an aid for visualizing gravitational field patterns. Recallthat g = | g | = 9.8 m/s2

Electric Field Lines • An aid for visualizing electric field patterns. • Point in the same direction as the electric field vector, E, at any point. • E is large when the field lines are close together, E is small when the lines are far apart.

Electric Field Lines • The lines begin on positive charges and terminate on negative charges, or at infinity in the case of excess charge. • The number of lines leaving a positive charge or approaching a negative charge is proportional to the magnitude of the charge. • No two field lines can cross. • E is in the direction that a positive test charge will tend to go.

+ Electric Field Lines • The lines begin on positive charges and terminate on negative charges, or at infinity in the case of excess charge.

- Electric Field Lines • The lines terminate on negative charges.

Electric Field Lines • More examples Field lines cannot cross!

Serway & Jewett, Principles of Physics, 3rd ed. Figure 19.20 See the discussion about this figure on page 683 in your book.

Serway & Jewett, Principles of Physics, 3rd ed. Figure 19.21 See Example 19.6 on page 684 in your book.

Serway & Jewett, Principles of Physics, 3rd ed. Figure 19.22 See Example 19.7 on page 685 in your book.

Work Done by a Constant Force (Review) • Fluffy exerts a constant force of 12N to drag her dinner a distance of 3m across the kitchen floor. • How much work does Fluffy do?

q Work Done by a Constant Force (Review) • Ingeborg exerts a constant force of 12N to drag her dinner a distance of 3 m across the kitchen floor. • q = 30o • How much work does Ingeborg do?

Similar to Serway & Jewett, Principles of Physics, 3rd ed. Figure 6.1 See page 179 in your book.

Work Done by a Force (Review) • Is there a general expression that will give us the work done, whether the force is constant or not? • Yes! • Assume that the object that is being moved is displaced along the x-axis from xi to xf. • Refer to Figure 6.7 and Equation 6.11 on p. 184. • = area under graph of Fx from xi to xf

y a ya mo d g mo yb b Gravitational Field • Consider the uniform gravitational field near the surface of the earth = g • Recall that g = | g | = 9.8 m/s2 Suppose we allow a “test mass” mo to fall from a to b, a distance d.

y a ya mo Suppose we allow a “test mass” mo to fall from a to b, a distance d . d g mo yb b Gravitational Field • How much work is done by the gravitational field when the test mass falls?

E Electric Field • A uniform electric field can be produced in the space between two parallel metal plates. • The plates are connected to a battery.

E qo qo a b d Electric Field • How much work is done by the electric field in moving a positive test charge (qo) from a to b?

E qo qo a b d Electric Field • Recall that FE = qo E • Magnitude of displacement = d

Potential Difference = Voltage • Definition • The Potential Difference or Voltage between points a and b is always given by • =(work done by E to move test chg. from a to b) • (test charge) • This definition is true whether E is uniform or not.

Potential Difference = Voltage • For the special case of parallel metal plates connected to a battery -- • The Potential Difference between points a and b is given by • This is also called the Voltage between points a and b. • Remember, E is assumed to be uniform.

Potential Difference = Voltage • We need units! • Potential Difference between points a & b ºVoltage between points a & b

Potential Difference = Voltage • More units! • Recall that for a uniform electric field so In your book’s notation: Where d is positive when the displacement is in the same direction as the field lines are pointing.

Potential Difference = Voltage • In the general case • = a “path integral” or “line integral” • Therefore

Potential Difference = Voltage • If E, FE, and the displacement are all along the x-axis, this doesn’t look quite so imposing! • So

Electric Fields, Voltage, Electric Current, and Ohm’s Law