Slide 1 / 101 Slide 2 / 101 Algebra Based Physics Electric Field, Potential Energy and Voltage 2015-11-30 www.njctl.org Slide 3 / 101 Slide 4 / 101 Electric Field, Potential Energy and Voltage Click on the topic to go to that section Electric Field · *Electric Field relationship to Gravitational Field · Electric Field Electric Field of Multiple Charges · **The Net Electric Field · Electric Potential Energy · Electric Potential (Voltage) · Uniform Electric Field · Return to Table of Contents https://www.njctl.org/video/?v=TDD4O-a1AF4 https://www.njctl.org/video/?v=OBin44Pm2g0 Slide 5 / 101 Slide 6 / 101 Electric Field Electric Field Let's find the Electric Field due to one charge. The notation in Coulomb's Law will be modified slightly - assuming that one The Electric Field starts with Coulomb's Law: charge is very large - and the other charge is a small, positive test charge that will have a negligible Electric Field due to its size. The large charge will be labeled, Q, and the small charge, q, and This gives the force between two charges, q 1 and q 2 . Similar to the distance between them is r. the gravitational force, no contact is needed between the two charges for them to feel a force from the other charge. The absolute value signs will be removed, as we will now consider the vector quality of the Force (note the arrow on the top This "action at a distance" is best understood by assuming that of the F - that means that F is a vector - it has magnitude and each charge has a field surrounding it that affects other charges - this is called the Electric Field. direction).
Slide 7 / 101 Slide 8 / 101 Electric Field Electric Field Q creates the electric field. The size of charge Q and the distance to a point determine the strength of the electric field (E) at that point. To find the Force that the large charge exerts on the little charge, the above equation will be divided by q, and this will be defined as the Electric Field. E is measured in N/C (Newtons per Coulomb). The Electric Field is represented as a group of lines that show its direction and strength - which is the Force that it would exert on a positive charge within its field. The Electric Field now shows both the magnitude and direction Hence, these Electric Field lines (which are imaginary, but help us of the force exerted by Q on any charge. To find the force, the visualize what is happening) originate on positive charges and end Electric Field is multiplied by the charge that is being considered. on negative charges. Slide 9 / 101 Slide 10 / 101 Electric Field Electric Field due to a Negative Charge due to a Positive Charge If there is an isolated positive charge, it will create an Electric If there is an isolated negative charge, it will create an Electric Field that points radially away from it in all directions, since a Field that points radially towards it in all directions, since a positive test charge in the field will be repelled by this charge. positive test charge in the field will be attracted by this charge. (electric field lines) Electric Field Force Electric Field Force on a small positive on a small positive (electric field lines) test charge test charge + - + + Slide 11 / 101 Slide 12 / 101 Electric Field Direction Michael Faraday and Magnitude The electric field is attributed to The definition of the Electric Michael Faraday. Faraday was born Field shows that the strength of in London in 1791. He came from a the field decreases as distance increases poor family. At 13, he apprenticed as + a book seller and binder while also attending local lectures on philosophical and scientific topics. This can be seen by looking at the density of the field lines. A member of the Royal Institute took notice of Faraday and bought him Note that the Electric Field lines are closer together (more dense) tickets to several Royal Institute when they are closer to the charge that is generating the Field. This indicates the Electric Field is greater nearer the charge. lectures. In 1813, he was invited to work at the Royal Institute where he made Click here to try a numerous contributions to physics and chemistry. simulator from PhET
Slide 13 / 101 Slide 13 (Answer) / 101 1 Find the magnitude of the electric field for a 1 Find the magnitude of the electric field for a charge of 5.6 nC at a distance of 3.0 m. charge of 5.6 nC at a distance of 3.0 m. Answer [This object is a pull tab] https://www.njctl.org/video/?v=9ZMQozvAe_w https://www.njctl.org/video/?v=9ZMQozvAe_w Slide 14 / 101 Slide 14 (Answer) / 101 2 A 4.5 mC charge experiences an electrical force 2 A 4.5 mC charge experiences an electrical force of 9.0 mN in the presence of an electric field. of 9.0 mN in the presence of an electric field. What is the magnitude of the electric field? What is the magnitude of the electric field? Answer [This object is a pull tab] https://www.njctl.org/video/?v=9-6gSvSik2Y https://www.njctl.org/video/?v=9-6gSvSik2Y Slide 15 / 101 Slide 15 (Answer) / 101 3 If E 0 is the Electric Field generated at a distance r from a 3 If E 0 is the Electric Field generated at a distance r from a charge Q, what is the Electric Field at a distance 2r? charge Q, what is the Electric Field at a distance 2r? Answer [This object is a pull tab] https://www.njctl.org/video/?v=lNtL0qbvQsA https://www.njctl.org/video/?v=lNtL0qbvQsA
Slide 16 / 101 Slide 16 (Answer) / 101 4 The direction of the Electric Field can be found by using: 4 The direction of the Electric Field can be found by using: A the direction of the gravitational force. A the direction of the gravitational force. B the direction that a positive test charge would B the direction that a positive test charge would accelerate. accelerate. C the direction that a negative test charge would C the direction that a negative test charge would Answer B accelerate. accelerate. [This object is a pull tab] https://www.njctl.org/video/?v=h5VHz4A01T0 https://www.njctl.org/video/?v=h5VHz4A01T0 Slide 17 / 101 Slide 17 (Answer) / 101 5 What is the direction of the Electric Field at points 1, 2, 3 5 What is the direction of the Electric Field at points 1, 2, 3 and 4? and 4? A up, right, down, left. A up, right, down, left. 1 1 B up, left, down, right. B up, left, down, right. Answer C down, right, up, left. C down, right, up, left. Q+ A Q+ 4 2 4 2 D down, left, up, right. D down, left, up, right. 3 3 [This object is a pull tab] https://www.njctl.org/video/?v=BodIViPml2g https://www.njctl.org/video/?v=BodIViPml2g Slide 18 / 101 Slide 18 (Answer) / 101 6 What is the direction of the Electric Field at points 1, 2, 3 6 What is the direction of the Electric Field at points 1, 2, 3 and 4? and 4? 1 1 A up, right, down, left. A up, right, down, left. B up, left, down, right. B up, left, down, right. Q- Q- 4 2 4 2 C down, right, up, left. C down, right, up, left. Answer D D down, left, up, right. D down, left, up, right. 3 3 [This object is a pull tab] https://www.njctl.org/video/?v=hzHAYXstOQk https://www.njctl.org/video/?v=hzHAYXstOQk
Slide 19 / 101 Slide 19 (Answer) / 101 7 What is the magnitude and direction of the electric 7 What is the magnitude and direction of the electric field at a distance of 2.3 m due to a charge of -4.9 field at a distance of 2.3 m due to a charge of -4.9 μC? μC? Answer Towards the charge [This object is a pull tab] https://www.njctl.org/video/?v=YhLxeo8POMg https://www.njctl.org/video/?v=YhLxeo8POMg Slide 20 / 101 Slide 21 / 101 *Electric Field relationship to Gravitational Field In the chapter on Electric Charge and Force, the similarity between the electric force and the gravitational force was noted. *Electric Field There is a similar relationship between the Electric Field and the relationship to the Gravitational Field. The reason for this is that the two forces are both central forces in Gravitational Field that they act along the line connecting objects. There is a key difference between the two fields and forces. Mass, which is the source of the gravitational field is always positive, and the force is always attractive. Charge, the source of the Electric Field can be negative or positive and the force is either attractive or Return to repulsive. Table of Contents https://www.njctl.org/video/?v=QxyeHM-I7LM Slide 22 / 101 Slide 23 / 101 *Electric Field relationship to *Electric Field relationship to Gravitational Field Gravitational Field Given that a mass m is located at the surface of the planet with a Gravity Electric Equivalencies between the Forces and Fields mass of M and radius R, Newton's Law of Universal Gravitation is used to determine the gravitational force, F G , between the planet and Newton's Law of Universal Coulomb's Law Gravitation mass m: Divide this expression by m (where m<<M) - similar to what was done with the small positive test charge, q, and call this "g,", the Gravitational Field: mass (kg) charge (Coulombs) distance, r, between centers of mass distance, r, between centers of charge Gravitational Field Electric Field This is used to express the "weight" of the mass m on the planet:
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