**Unit 10: Static
Electricity**

**Problem Set A**

**Overview:**

Problem Set A targets your ability to use equations related to electric charge, electric force and electric field intensity. There are 20 problems in this problem set which range in difficulty from the very easy to rather difficult. To be successful, you will need to understand at least three quantitative ideas. They are:

**Relating the Quantity of Charge to Numbers of Protons and Electrons**Atoms are the building blocks of all objects. These atoms possess protons, neutrons and electrons. While neutrons are electrically neutral, the protons and electrons in an atom possess electrical charge. The proton and electron have a predictable amount of charge, with the proton being assigned a positive type of charge and the electron a negative type. The charge on an electron has a well-accepted, experimentally-determined value of -1.6 x 10

^{-19}C (where the negative simply indicates the type of charge). Protons have an equal amount of charge and an opposite type; thus, the charge of a proton is +1.6 x 10^{-19}C. Objects consisting of atoms containing protons and electrons can have an overall charge on them if there is an imbalance of protons and electrons. An object with more protons than electrons will be charged positively and an object with more electrons than protons will be charged negatively. The magnitude of the quantity of charge on an object is simply the difference between the number of protons and electrons multiplied by 1.6 x 10^{-19}C.

**Coulomb's Law of Electric Force**A charged object can exert an attractive or repulsive force on other charged objects in its vicinity. The amount of force follows a rather predictable pattern which is dependent upon the amount of charge present on the two objects and the distance of separation. Coulomb's law of electric force expresses the relationship in the form of the following equation:

**F**_{elect}= k•Q_{1}•Q_{2}/d^{2}where

**F**represents the magnitude of the electric force (in Newtons),_{elect}**Q**and_{1}**Q**represent the quantity of charge (in Coulombs) on objects 1 and 2, and_{2}**d**represents the separation distance between the objects' centers (in meters). The symbol**k**represents a constant of proportionality and has the value of 9.0 x 10^{9}N•m^{2}/C^{2}.

**Electric Field**A charge object can exert an electric influence upon objects from which they are spatially separated. This action-at-a-distance phenomenon is sometimes explained by saying the charged object establishes an electric field in the space surrounding it. Other objects which enter the field interact with the field and experience the influence of the field. The strength of the electric field can be tested by measuring the force exerted on a test charge. Of course, the more charge on the test charge, the more force which would be experienced by it. While the force experienced by the test charge is proportional to the amount of charge on the test charge, the ratio of force to charge would be the same regardless of the amount of charge on the test charge. By definition, the electric field strength (

**E**) at a given location about a source charge is simply the ratio of the force experienced (**F**) by a test charge to the quantity of charge on the test charge (**q**)._{test}**E = F / q**_{test}The electric field strength as created by a source charge (

**Q**) varies with location. In accord with Coulomb's law, the force on a test charge is greatest when closest to the source charge and less when further away. Substitution of the expression for force into the above equation and subsequent algebraic simplification yields a second equation for electric field (**E**) which expresses its strength in terms of the variables which effect it. The equation is**E = k • Q / d**^{2}where

**k**is Coulombs constant of 9.0 x 10^{9}N•m^{2}/C^{2},**Q**is the quantity of charge on the source creating the field and**d**is the distance from the center of the source.

In addition to an understanding of the above mathematical quantities of charge, force and field, success on this problem set is dependent upon a conceptual understanding of the following principles.

**Direction of Force and Field Vectors**Many problems on this problem set will demand that you understand the directional nature of electric force and electric field. Electric forces between objects can be attractive or repulsive. Objects charged with an opposite type of charge will be attracted to each other and objects charged with the same type of charge will be repelled by each other. These attractive and repulsive interactions describe the direction of the forces exerted upon any object. In some instances involving configurations of three or more charges, an object will experience two or more forces in the same or different directions. In such instances, the interest is usually in knowing what the net electric force is. Finding the net electric force involves determining the magnitude and direction of the individual forces and then adding them up to determine the net force. When adding electric forces, the direction must be considered. A 10 unit force to the left and a 25 unit force to the right add up to a 15 unit force to the right. Such reasoning about direction will be critical to analyzing situations where two or more forces are present.

Electric field is also a vector quantity that has a directional nature associated with it. By convention, the direction of the electric field vector at any location surrounding a source charge is in the direction that a positive test charge would be pushed or pulled if placed at that location. Even if a negative charge is used to measure the strength of a source charge's field, the convention for direction is based upon the direction of force on a positive test charge.

**Comparing Gravitational and Electrical Forces**Gravitational forces and electrical forces are often compared to each other. Both force types are fundamental forces which act over a distance of separation. Gravitational forces are based on masses attracting and follow the law of universal gravitation equation.

**F**_{grav}= G • m_{1}• m_{2}/ d^{2}where

**m**and_{1}**m**are the masses of the attracting objects (in kg),_{2}**d**is the separation distance as measured from object center to object center (in meters) and**G**is a proportionality constant with a value of 6.67x 10^{-11}N•m^{2}/kg^{2}.Electrical forces are based on charged objects attracting or repelling and follow Coulomb's law equation (as stated above). Some of the problems on this set will involve comparisons of the magnitude of the electric force to the magnitude of the gravitational force. The simultaneous use of both equations will be necessary in the solution of such problems.

**Additional Readings/Study
Aids:**

The following pages from The Physics Classroom tutorial may serve to be useful in understanding the mathematics of electric force and electric field.

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