Slide 1 / 33. Electric Charge and Electric Field

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1 Slide 1 / 33 Electric Charge and Electric Field

2 Slide 2 / 33 Electric Charge When you rub a rod with a piece of fur both objects become charged and you can pick up small pieces of paper. This natural phenomenon was first discovered by the Greeks around 600 B.C. when they rubbed amber with wool. Today we know that there are two types of charges, we call them positive and negative. To demonstrate electrostatics, the interactions between charged objects which are nearly at rest, we will use a plastic and glass rod, and silk and fur cloths. When we rub the plastic rod with a piece of fur the rod becomes negatively charged and the fur becomes positively charged. When we rub the glass rod with a piece of silk the rod becomes positively charged and the silk becomes negatively charged. After conducting several experiments with these charged objects we can determine that like charges repel, and unlike charges attract.

3 Slide 3 / 33 Structure of the atom When we rub two objects together, why does one attain a positive charge and the other one a negative charge? The answer lies in the structure of the atom. As you already know an atom is comprised of electrons, protons, and neutrons. The protons and neutrons are located in the dense center of the atom called the nucleus and the electrons orbit about it in the electron cloud. When the two objects are rubbed the electrons are essentially pulled out of their energy levels. This results in positively and negatively charged objects. The protons do not move because they are fixed within the nucleus, the electrons move and the object that loses them ends up being positively charged.

4 Slide 4 / 33 Conservation of Charge and the smallest natural unit of charge Conservation of charge states that charge cannot be destroyed nor created. This is similar to conservation of energy. Therefore, the two objects rubbed together have the same magnitude of charge, but opposite signs. This is why we consider charges to be positive and negative, because when we add them we should find what the net charge is. In this case it would be zero because both objects were originally neutral. The second law is that the charge of the electron and proton is the smallest unit of charge possible (1.6*10-19 C). Meaning every charge is an integer of the charge of the electron and proton.

5 Slide 5 / 33 1 A plastic rod is rubbed with a piece of wool. During the process the plastic rod acquires a positive charge and the wool: A B C D E acquires an equal positive charge acquires an equal negative charge acquires less in magnitude positive charge acquires less in magnitude negative charge remains neutral

6 Slide 6 / 33 Conductors and Insulators A conductor is an element or material which allows the free flow of charge. If a metal sphere is given a charge Q, that charge will be uniformly distributed over the surface of the sphere. This is because the charges repel one another and the material will not hinder the charges movement so they are able to move all the way to the surface. A insulator is an element or material which prevents charge from freely flowing. If a charge Q is uniformly distributed throughout the spherical insulator, the charge will remain where it is because even though the charges repel one another the insulator prevents them from moving.

7 Slide 7 / 33 2 A conducting sphere is charged with a negative charge - Q. Which statement about the charge distribution is correct? A B C D E Charge in concentrated at the center of the sphere Charge is concentrated at the bottom part of the sphere Charge is evenly distributed throughout the volume of the sphere Charge is evenly distributed on the surface of the sphere More information is required

8 Slide 8 / 33 Induction vs. Conduction Induction is the process of charging an objecting without contact. Induction If a positively charged rod is brought close to a neutral metal sphere the rod will induce a charge on the sphere's surface. The negative charges in the sphere will be attracted towards the rod, while the positive charges are repelled. If a negatively charged rod is brought close to a neutral metal grounded sphere, the positive charges will be attracted and the negative charges will be forced through the wire into the earth. The wire is then removed and the rod is taken away. The sphere now has an induced positive charge. Conduction is the process of charging an objecting through contact, and the charge will flow until the electric potential of both objects is equal. Conduction

9 Slide 9 / 33 3 A positively charged sphere is brought near end A of the uncharged metal bar shown below. Ends A and B of the metal bar will be charged: A B C D E positive, negative negative, positive positive, positive negative, negative neutral, neutral

10 Slide 10 / 33 4 A neutral electroscope is touched by a positively charged rod and then the rod is removed. Afterwards a negatively charged rod is brought close to the electroscope. What happens to the leaves of the electroscope? A B C The leaves move closer together The leaves move further apart The leaves remain were they are

11 Slide 11 / 33 5 A neutral electroscope is grounded using a wire. A positively charged rod is brought close to the electroscope and after a while the wire is cut and the rod is removed. Afterwards a negatively charged rod is brought close to the electroscope. What happens to the leaves of the electroscope? A B C The leaves move closer together The leaves move further apart The leaves remain were they are

12 Slide 12 / 33 6 A student in a physics lab wants to determine the type of an electric charge on an initially charged electroscope. He brings two charged rods near the electroscope without touching it. The positively charged rod causes the leaves to move further apart and the negatively charged rod causes the leaves to move closer to each other. What type of electric charge was initially on the electroscope? A B C D E positive negative neutral couldn't be determined because the electroscope wasn't grounded couldn't be determined because the electroscope wasn't isolated

13 Slide 13 / 33 Coulomb's Law The magnitude of the force exerted on two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The proportionality constant K is determined using almost the same apparatus that Cavendish used to determine the Gravitational Constant. From now on we will use this variation of the equation for simplicity.

14 Slide 14 / 33 7 Two charged objects with an equal charge of Q are separated by a distance r and attract each other with a certain force. If the charges on both objects are doubled and the separation is halved, the force between them will be: A B C D E 4 times greater 2 times greater 4 times less 16 times greater 16 times less

15 Slide 15 / 33 8 Two identical conducting spheres are charged to +Q and -3Q and separated by a distance r. The attractive force between the spheres is F. The two spheres are brought in a brief contact and then moved to their original positions. If the new electrostatic force between the spheres is F', which of the following is true? A B F = F' F' = 3F C F' = F/3 D F' = 9F E F' = F/9

16 Slide 16 / 33 9 What is the magnitude of the net force on charge C due to charges A and B? A B C D E

17 Slide 17 / 33 Electric Field and Electric Forces When two positively charged objects are placed a distance d apart from each other they exert a force on one another. Why? d They each generate their own electric field which produces an actionat-a-distance force. The Electric Field is defined as the electric force per unit of charge. (Electric Field due to a point charge) Electric Field lines radiate outward from a positive charge Electric Field lines radiate inward for a negative charge

18 Slide 18 / An electric charge Q is placed at the origin. If the magnitude of the electric field at point A is E, what is the electric field at point B? A B C 4E 2E E D E/2 E E/4

19 Slide 19 / A small sphere with charge q and masss m is attached to one end of an insulating string of length L. The other end is attahed to a negatively charged wall. The electric field E due to the charged wall is constant in the vicinity of the charged sphere. The string makes a constant angle of with the vertical. What is the sign and magnitude of charge q? A B C D E Positive and a magnitude of Positive and a magnitude of Negative and a magnitude of Negative and a magnitude of Negative and a magnitude of

20 Slide 20 / 33 Principle of Superposition of Electric Fields Previously we talked about solving for the electric field of a single point charge, but what if more than one charge is in the same area? + E 1 + P E 3 E 2 - The net electric field at point p is the vector sum of each charges electric field. This principle can be extended onto charge distributions with a linear, surface, or volumetric charge density.

21 Slide 21 / What is the direction of the net electric field at Point P? A B C D E

22 Slide 22 / A point charge = 4.0 is placed at point -2m. A second charge is placed at point +3m. The net electric field at the origin is zero. What is charge? A Positive 9.0 B Positive 6.0 C Positive 3.0 D Negative 6.0 E Negative 9.0

23 Slide 23 / 33 Electric Field Calculations for charged objects We reviewed how to calculate an electric field due to several point charges, but what if you are asked to find the electric field a distance x away from the center of a uniformly charged ring of radius a. a P x After we draw out the picture for this case the next question is how to account for the charge. If we had hundreds of point charges placed in a circle we could calculate the electric field at a certain distance away from its center. So for the ring that is what we will do, we will cut up the overall ring into small pieces with a charge dq and find the electric field due to each.

24 Slide 24 / 33 Electric Field Calculations for charged objects dq r a θ P de x x de y de We proved before that: For charge distributions we will use: For the ring the net Electric field is in the x-direction because every component of the electric field cancels out in the y-direction. We are now ready to solve for the net Electric Field.

25 Slide 25 / 33 dq a r θ P de x x de y de

26 Slide 26 / 33 Electric Dipoles An electric dipole is a combination of point charges with the same magnitude, but opposite sign separated by a distance d. An example of a Electric Dipole is a water molecule. H + O H - The covalent bond which holds the water molecule together shifts some of the charge resulting in a polar molecule, the electric dipole.

27 Slide 27 / 33 Torque on Electric Dipoles When an electric dipole is placed within a uniform electric field we can think of the two sides as separate positive and negative charges. The force acting on them will be equal, F = Eq, but the direction of the forces will result in a net torque about its dipole axis causing the dipole to align with the electric field. H + H Dipole Axis d + - O -

28 Slide 28 / 33 Torque on Electric Dipoles Torque on Positive End Torque on Negative End clockwise clockwise Resulting in: If the distance between the charges is perpendicular to the direction of the two forces, the dipole moment is defined as:

29 Slide 29 / 33 Torque on Electric Dipoles Torque can be represented as into vector form. or it can be turned The vector of the dipole moment follows the dipole axis and points from the negative to the positive charge Using the right hand rule for the vector product we see that if the force is parallel to the dipole axis the torque on the dipole is zero and if it is perpendicular then the torque is at its greatest.

30 Slide 30 / 33 Work done by the Electric Field on an Electric Dipole Before we covered that the change in work with respect to the angle is equal to the torque. Since the force is resulting in a decrease in the torque, when we substitute for we make it negative. Know if we integrate with respect to the angel the dipole moves through we can find the work done by the force during that movement.

31 Slide 31 / 33 Potential Energy of an Electric Dipole Work is the negative change of potential energy therefore: It can also be rewritten as a scalar product:

32 Slide 32 / 33 Electric Field of an Electric Dipole A dipole can be represented by two separate point charges spaced a certain distance away. The electric field for the dipole is simply the vector sum of the two particles.

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