24. Electric Force & Field; Gauss' Law

Coulomb's Law (Electric Force)

Electric Charge and Electric Fields

Three point charges are arranged along the x-axis. Charge q1 = +3.00 mC is at the origin, and charge q2 = -5.00 mC is at x = 0.200 m. Charge q3 = -8.00 mC. Where is q3 located if the net force on q1 is 7.00 N in the -x-direction?

Coulomb's Law (with example)

Coulomb's law

left; 3.8×1014 m/s2

left; 6.2×1013 m/s2

left; 6.2×109 m/s2

right; 1.1×1015 m/s2

In which direction will the −1 C charge move? If it has a mass of 10 g, what will its initial acceleration be?<img src="https://static.studychannel.pearsonprd.tech/courses/physics/thumbnails/images/17f8e2c2"alt=""/>

Just How Strong Is the Electric Force? Suppose you had two small boxes, each containing 1.0 g of protons. (a) If one were placed on the moon by an astronaut and the other were left on the earth, and if they were connected by a very light (and very long!) string, what would be the tension in the string? Express your answer in newtons and in pounds. Do you need to take into account the gravitational forces of the earth and moon on the protons? Why? (b) What gravitational force would each box of protons exert on the other box?

Anderson Video - Coulomb's Law Example with Two Charges

A <math display=“inline”><mrow><mn>3</mn><mo>.</mo><mn>0</mn><mtext>&#x00A0;</mtext><mtext>nC</mtext></mrow></math> charge is at the origin, a <math display=“inline”><mrow><mo>&#x2212;</mo><mn>12</mn><mtext>&#x00A0;</mtext><mtext>nC</mtext></mrow></math>charge is at <math display=“inline”><mrow><mi>x</mi><mo>=</mo><mrow><mn>2.0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">cm</mi></mrow></mrow></math>. Where, on the x-axis, could you place a <math display=“inline”><mrow><mo>&#x2212;</mo><mn>45</mn><mtext>&#x00A0;</mtext><mtext>nC</mtext></mrow></math>charge so that it would experience no net force?

Coulomb's Law Problems

Electroscope (Find Charge)

Coulomb's Law

What is the distance between a <math display=“inline”><mrow><mn>10</mn><mtext>&#x00A0;</mtext><mi>&#x03BC;</mi><mi mathvariant="normal">C</mi></mrow></math> charge and a <math display=“inline”><mrow><mn>24</mn><mtext>&#x00A0;</mtext><mi>&#x03BC;</mi><mi mathvariant="normal">C</mi></mrow></math> charge if the magnitude of the force between them is <math display=“inline”><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mtext>&#x00A0;</mtext><mtext>mN</mtext></mrow></math>?

Two small spheres spaced 20.0 cm apart have equal charge. How many excess electrons must be present on each sphere if the magnitude of the force of repulsion between them is 3.33 * 10^-21 N?

Exploiting Symmetry

Coulomb's Law (1 of 7) An Explanation

Anderson Video - Coulomb's Law Example with Three Charges

Two small aluminum spheres, each having mass 0.0250 kg, are separated by 80.0 cm. (c) What fraction of all the electrons in each sphere does this represent?

Anderson Video - Hydrogen Atom

Three point charges are arranged on a line. Charge q3 = +5.00 nC and is at the origin. Charge q2 = -3.00 nC and is at x = +4.00 cm. Charge q1 is at x = +2.00 cm. What is q1 (magnitude and sign) if the net force on q3 is zero?

Two small plastic spheres are given positive electric charges. When they are 15.0 cm apart, the repulsive force between them has magnitude 0.220 N. What is the charge on each sphere (a) if the two charges are equal and

Coulomb's Law (2 of 7) Calculate the Force Between Two Charges

There is a <math display=“inline”><mrow><mo>&#x2212;</mo><mn>4.00</mn><mtext>&#x00A0;</mtext><mtext>nC</mtext></mrow></math>charge at the origin. A <math display=“inline”><mrow><mn>9</mn><mo>.</mo><mn>00</mn><mtext>&#x00A0;</mtext><mtext>nC</mtext></mrow></math> charge is on the x-axis at <math display=“inline”><mrow><mi>x</mi><mo>=</mo><mrow><mn>2.00</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">m</mi></mrow></mrow></math>. A <math display=“inline”><mrow><mn>5.00</mn><mtext>&#x00A0;</mtext><mtext>nC</mtext></mrow></math> charge is on the y-axis at <math display=“inline”><mrow><mi>y</mi><mo>=</mo><mo>&#x2212;</mo><mrow><mn>1.00</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">m</mi></mrow></mrow></math>. What is the total force on the <math display=“inline”><mrow><mo>&#x2212;</mo><mn>4.00</mn><mtext>&#x00A0;</mtext><mtext>nC</mtext></mrow></math> charge at the origin? Give your answer as a magnitude and an angle counterclockwise from the positive x-axis.

Charges In A Line (Find Zero Force)

What is the relationship between the gravitational force between two electrons, <math display=“inline”><mrow><msub><mi>F</mi><mtext>G</mtext></msub></mrow></math>. and the electric force between two electrons, <math display=“inline”><mrow><msub><mi>F</mi><mtext>E</mtext></msub></mrow></math>?

Two small aluminum spheres, each having mass 0.0250 kg, are separated by 80.0 cm. (b) How many electrons would have to be removed from one sphere and added to the other to cause an attractive force between the spheres of magnitude 1.00 * 10^4 N (roughly 1 ton)? Assume that the spheres may be treated as point charges.

If the force between two charges is F when the distance is d, what will the force between the two charges be if they were moved to a distance of 2d?

Introduction to Coulomb's Law or the Electric Force

Charges in a Plane

Charges In A Triangle (Rank Force Pairs)

The net force is 0 so its direction is undefined

What is the direction of the net force on the charge at the center of the square in the following figure?<img src="https://static.studychannel.pearsonprd.tech/courses/physics/thumbnails/images/f7751ee5"alt=""/>

Two small plastic spheres are given positive electric charges. When they are 15.0 cm apart, the repulsive force between them has magnitude 0.220 N. What is the charge on each sphere (b) if one sphere has four times the charge of the other?

Anderson Video - Atoms and Coulomb's Law

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