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## Physics 2112 Unit 6: Electric Potential

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**Physics 2112Unit 6: Electric Potential**Today’s Concept: Electric Potential (Defined in terms of Path Integral of Electric Field)**Last time we defined the electric potential energy of**charge q in an electric field: Big Idea The only mention of the particle was through its charge q. We can obtain a new quantity, the electric potential, which is a PROPERTY OF THE SPACE, as the potential energy per unit charge. Note the similarity to the definition of another quantity which is also a PROPERTY OF THE SPACE, the electric field.**Example 6.2a (Potential from Field)**A +8uC charge is placed in a downwards pointing electric field with a magnitude of 6N/C. An outside force moves the charge up a distance of 0.4m from point 1 to point 2. = 6 N/C q=+8uC a) What is the force on this charge? b) How much work was done by the outside force during this move?**Example 6.2.b (Potential from Field)**A +8uC charge is placed in a downwards pointing electric field with a magnitude of 6N/C. An outside force moves the charge up a distance of 0.4m from point 1 to point 2. = 6 N/C q=+8uC c) How much work was done by the electric field during this move? d) What is the change in the electrical potential energy of the particle?**Example 6.2.c (Potential from Field)**A +8uC charge is placed in a downwards pointing electric field with a magnitude of 6N/C. An outside force moves the charge up a distance of 0.4m from point 1 to point 2. = 6 N/C q=+8uC e) What is the difference in electrical potential between points 1 and 2? f) What is the electrical potential at point 2?**Consider the three points A, B, and C located in a region of**constant electric field as shown. Electric Potential from E field D Dx What is the sign of DVAC= VC-VA? A) DVAC< 0 B) DVAC= 0C) DVAC> 0 Choose a path (any will do!)**CheckPoint: Zero Electric Field**• Suppose the electric field is zero in a certain region of space. Which of the following statements best describes the electric potential in this region? • The electric potential is zero everywhere in this region. • The electric potential is zero at least one point in this region. • The electric potential is constant everywhere in this region. • There is not enough information given to distinguish which of the above answers is correct. Remember the definition**Example 6.2 (V from point charges)**-5nc +5nc B A x 10cm 10cm 10cm +Q -Q What is the electrical potential at points A and B? Define V = 0 at r = (standard)**Example 6.3 (V from point charges)**C -5nc +5nc 10cm x +Q -Q 10cm 20cm What is the electrical potential at point C? Define V = 0 at r = (standard)**If we can get the potential by integrating the electric**field: E from V In Cartesian coordinates: We should be able to get the electric field by differentiating the potential?**Example 6.4 (E-field above a ring of charge)**What is the electrical potential, V, a distance yabove the center of ring of uniform charge Q and radius a? (Assume V = 0 at y = ) P y x y What is the electrical field, E, at that point? a**CheckPoint: Spatial Dependence of Potential 1**The electric potential in a certain region is plotted in the following graph • At which point is the magnitude of the E-FIELD greatest? • A • B • C • D**CheckPoint: Spatial Dependence of Potential 2**The electric potential in a certain region is plotted in the following graph • At which point is the direction of the E-field along the negative x-axis? • A • B • C • D**Example 6.5 (DV near line of charge)**An infinitely long solid insulating cylinder of radius a = 4.1 cm is positioned with its symmetry axis along the z-axis as shown. The cylinder is uniformly charged with a charge density ρ = 27.0 μC/m3. Concentric with the cylinder is a cylindrical conducting shell of inner radius b = 19.9 cm, and outer radius c = 21.9 cm. The conducting shell has a linear charge density λ = -0.36μC/m. What is V(P) – V(R), the potential difference between points P and R? Point P is located at (x,y) = (46.0 cm, 46.0 cm). Point Ris located at (x,y) = (0cm, 46.0 cm).**Point charge q at center of concentric conducting spherical**shells of radii a1, a2, a3, and a4.The inner shell is uncharged, but the outer shell carries charge Q. What is V as a function ofr? Example 6.5 (DV for charges) cross-section a4 a3 +Q a2 a1 +q metal metal • Main Idea: • Charges q and Q will create an E field throughout space • Plan: • Spherical symmetry: Use Gauss’ Law to calculate E everywhere • Integrate E to get V**Equipotentials**In previous example, all these points had same V, same electrical potential Line is called “equipotenial” or “a line of equipotential”.**Topographic Map**Lines on topo map are lines of “equal gravitational potential” Closer the lines are, the steeper the hill Gravity does no work when you walk along a brown line.**Equipotentials**Equipotentials produced by a point charge Equipotentials always perpendicular to field lines. SPACINGof the equipotentials indicates STRENGTHof the Efield.**CheckPoint: Electric Field Lines 1**The field-line representation of the E-field in a certain region in space is shown below. The dashed lines represent equipotential lines. • At which point in space is the E-field the weakest? • A • B • C • D**CheckPoint: Electric Field Lines 2**The field-line representation of the E-field in a certain region in space is shown below. The dashed lines represent equipotential lines. • Compare the work done moving a negative charge from A to B and from C to D. Which one requires more work? • More work is required to move a negative charge from A to B than from C to D • More work is required to move a negative charge from C to D than from A to B • The same amount of work is required to move a negative charge from A to B as to move it from C to D • Cannot determine without performing the calculation