Ph 12 Electrostatics

Physics 12 — Electrostatics

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V 1 — Electrostatic Forces Electric charge is a property of protons (positive) and electrons (negative). Electrostatics is a study of the forces and energy of charges that are not moving. An electric charge is due to an unbalanced amount of protons and electrons. Like electric charges repel and unlike electric charges attract. A conductor is an object that will allow charges (usually electrons) to move freely: metals, graphite, salt water… Because of their very small mass, usually the charge that moves is the electron. An insulator is an object that does not allow the free movement of charges (electrons): most organic materials, water… A charge is most easily generated by friction between two materials that have a different attraction for electrons. One will develop an excess of electrons and be charged negatively. The other will have a deficit of electrons and be charged positively. The total charge is conserved. An electroscope is a simple devise that can detect charges.


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An electroscope that has an unequal number of protons and electrons will show a charge. It is a charged electroscope. An electroscope with zero net charge can show a charge if the charges are not distributed evenly. This is an induced charge. Example 1: Show how a charged balloon can be attracted to a neutral wall, or how neutral sawdust will attract to a charged object. A charged electroscope can be neutralized by grounding it (earthing). The earth is considered to be able to donate or accept any number of electrons to neutralize any charge. An induced charge can be used to generate a charge. This animation shows: Induced charge Grounding Equalization of charge What is actually occurring as the positive charge neutralizes?


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Example 2: Explain why a Van de Graaf generator uses a sphere to store charge rather than a cube or an ellipsoid. The quantitative relationship for the force between two point charges is Coulomb’s Law:

F = force (N), Q = charge in coulombs (C), d = distance between point charges (m). k = 9.00 x 109 Nm2/C2 The charges must be point charges (or non-point charges from a large distance). The sign convention: A positive electrostatic force is a repulsive force. A negative force is an attractive force. Example 3: Find the electrostatic force between two stationary electrons 8.0 µm apart. What is the instantaneous acceleration if one of the electrons is released?

F

e=

kQ1Q

2

r 2


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Example 4: Three protons are placed on a line at 0 m, 0.40 m, 0.90 m. Find the force on each proton. Example 5: Three 35 µC charges are placed on the corners of an equilateral triangle with sides of 15 cm. What is the force on each charge? Example 6: 180 µC charges are placed at the corners of a 0.50 m square. The charges alternate from positive to negative. What is the force on each charge? pp. 496-501, Q 4, 5, 7, 8 P 1, 4, 5, 7, 11-14, 18, 19


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V 2 — Electric Fields An electric field (E) represents the effects that electric charges would have on an external electric charge if it were placed at a specific point in space. To determine the electric field, a very small positive test charge (q) is placed at a point and the force on that test charge is measured. The electric field is measured in Newtons per coulomb (N/C). The direction of the electric field is the same direction as the force on the test charge. A very small test charge is used because a large test charge would alter the electric field that it is trying to measure. For a point charge, the electric field can be calculated from Coulomb’s Law:

The electric field depends on the size of the point charge and the distance from the charge. The direction will depend on the sign of the charge. V 2 — Electric Fields Here is the electric field for a positive and a negative point charge. It is a radial field. Larger charge:

E =F

q

E =F

q=

kQq

r 2

1

q

!"#

$%&=

kQ

r 2


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Electric fields from multiple sources can be added as vectors. The field from each source is determined, and the net field found by vector addition.

This is the field from two equal positively charged point charges.

Example 1: Draw the electric field lines for two equally charged negative charges.


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Example 2: Draw the electric field lines for two charges of equal magnitude but opposite charge. If the charges are not equal, the larger charge will have a larger affect on the net field. As a result, the field around the larger charge will be less distorted, and the field around the smaller charge will be more distorted. The larger charge should also have a greater density of field lines around it. Example 3: Draw field lines for: +q, +3q -q, -3q +q, -3q +3q, -q Draw in order given to match key.


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Example 4: Two 20 µC charges are 0.50 m apart on a horizontal line. Find the electric field: a) Between the two charges b) 0.20 m above one of the charges. Example 5: Find the acceleration of an electron in a 35 N/C electric field that is directed North..


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The field between two parallel plates is nearly uniform between the plates (considered uniform). It is distorted at the plate edges. A uniform field makes many calculations easier.

Example 6: Two parallel plates are 15 mm apart with a 200 N/C field between them. How much work would be required to move a proton from one plate to the other? pp. 496-501, Q 14, 15, 18, 19 P 21, 23, 25, 30, 31, 34, 38, 49

V 3 — Electric Potential Electric Potential Energy for point charges is calculated very similarly to gravitational potential energy.

Zero energy is at infinite distance. Because charges can be positive or negative, potential energy can be positive of negative.

E

p=

kQ1Q

2

r


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V =

kQ

r

Example 1: Calculate the work required to bring a proton from far away to 1.0 mm from a 30 µC charge. What is the work if the proton is replaced with an electron? Electric potential (or potential) is a measure of the potential energy change per coulomb of charge. It is measured in Volts (V) or J/C. If a charge q is moved so its potential energy changes: From a point charge the voltage is: As voltage is a scalar quantity. If there are more than one charge, find the voltage from each charge and add them to find the total voltage. V 3 — Electric Potential Example 2: Find the potential difference from 1.0 m to 0.l0 m from a 200 µC charge. What work would be required to move a proton through this difference? Why can W = Fd not be used here?

!V =!PE

q


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Example 3: Two 20 µC charges are 0.50 m apart on a horizontal line. Find the electric potential: a) Between the two charges b) 0.20 m above one of the charges. Example 4: An electron is accelerated in a T.V. tube by an 50,000 V potential difference. What is the speed of the electrons as they hit the screen of the T.V.?


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To deal with very small amounts of energy the electron volt (eV) was invented. This is the energy an electron gains if it is moved through a one volt difference. ∆PE = q∆V 1 eV = 1.6 x 10-19J It is often easiest to convert electron volts to joules for work in calculations. In between two charged parallel plates, the electric field is uniform. The work to move a charge between the plates is:

W = ∆PE W = q∆V Fd = q∆V

Eqd = q∆V E = ∆V/d

The electric field can be expressed in Volts per meter (V/m) as well as N/C. Example 5: A 0.0040 kg mass is held stationary by two horizontal plates with a ∆V of 10,000V. If the plates are 25 cm apart, what must be the charge on the mass to hold it stationary? A simple cathode ray tube uses a voltage difference to accelerate electrons and a voltage difference to deflect electrons.

pp. 522-525, Q 1, 4, 5, 7 P 1, 3, 5, 9, 13, 15, 19, 21

d !V

d

Va

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Ph 12 Electrostatics