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- Electric Fields 3. A plastic rod is bent into the quarter circle of radius R as shown below. A total positive charge of Q is evenly distributed along the rod. a. In terms of the given quantities, what is the linear charge density A? b. Set up the two integrals you would evaluate to find the components of the electric field. The integrals should be written in terms of the given quantities {Q and R} Ex Ey с. Evaluate your integrals to write down the electric field vector at the origin. y E = -f 10 + +B. Solve the problem. Show your complete solution. 1. What is the magnitude of a point charge that would create an electric field of 1.00 N/C at points 1.00 m away?Part D. Integrate your expressions for dEx and dEy from θ=0 to θ=π. The results will be the x-component and y-component of the electric field at P. Express your answers separated by a comma in terms of some, all, or none of the variables Q and a and the constants k and π. Part E. Use your results from part D to find the magnitude and direction of the field at P. Part F. What would be the electric field at P if the semicircle were extended to a full circle centered at P?
- Two very long solid cylindrical conductors of radius s run parallel with each other (on the same plane), with a separation of 2d (d>s) from their axes. What is the electric field in the midpoint between them if one of the cylinders has a charge distribution A and the other has –A? а. TEod towards the negative cylinder b. TEgd' towards the positive cylinder C. Zero d. Cannot be determinedL/2+ L/2 Note: Figure not drawn to scale. 1. A very long, thin, nonconducting cylinder of length L is centered on the y-axis, as shown above. The cylinder has a uniform linear charge density +2.. oint. is located on the y-axis at y = c, where L >> ¢. a) Kecling.c Abh ri gle Circle GEOMETRY AND TRIGONOMETRY i. On the figure shown below, draw an arrow to indicate the direction of the electric field at point F due to the long cylinder. The arrow should start on and point away from the dot. ii. escribe the shape and location of a Gaussian surface that can be used to determine the electric field at point P due to the long cylinder. iii. Use your Gaussian surface to derive an expression for the magnitude of the electric field at point P. E press your answer in terms of 2, c, L, and physical constants, as appropriate. A==bh A = r² C = 277 =r8 Rectangular Solid Vi h Cy.inder Sphere V = r²t Sm V=² S-427² sine Rig Triangle 2+6²=c² cos@= tan= +2 BIL a b C 2x. Q b ADVANCED PLACEMENT PHYSICS C…6:46 M CU. NO IT Part 1: The Charged Semi-Circular Hoop A thin plastic rod is bent into the shape of a semicircle of radius a. It is charged negatively with -Q Coulombs of charge. Show how to derive the equation for the electric field at the origin of the coordinate axes in the following diagram. 0 Tif. L. 18 dq ACORITONY 1. Identify the position vector for a small portion of the source charge distribution and express it in plane polar coordinates using a unit vector in those coordinates. f the fold O <
- I. Identify whether the statements below are correct or not. Write YES if the statement is correct, and NAH if the statement is wrong. ANSWER The flow of an electric field thru a given area is measurable using electric flux. If the field lines are close to each other, the electric field is stronger. The area or field around a charge where the electric flux can be experienced is called the electric field. The unit for electric flux is N.m²/C? If the field lines are close to each other, the electric field is weaker.Explain, giving detailed steps, how you would deter: une the electric field vector at point P. Give an expression for the electric field vector at point P if | q|= 0.1 nC and a = 0.001 metre.L d. A rod of length L on the y-axis has been non-uniformly charged with charge density given by å = ay where a has units of C/m and the total charge on the rod is Q. Answer the following questions as if you were being asked to find the electric field at the origin. Question 5 In general when we want to find the electric field from a continuous charge kdq The first step is distribution we start by setting up the general formula dE = to find dq for our particular situation. How would you write dq in terms of your chosen integration variable and other information given in the problem? %3D O a) dq = ay dy
- A solid ball with a 0.5m radius has 10uC charges in its center. Determine the electrical flux pass through the solid ball. a.) What is the electric field on the surface? b.) What is the electric flux that passes through the area? c.) What is the measure of the angle formed by vector dA and electric field? d.) What is the surface area of the sphere?a. Some discussions in the web refer electric field lines as“lines of force”. Discuss the advisability of thisdescription.b. Can an electric field exist in a region of space in whicha electric charge would not experience a force? Explain.Electric field lines are computed with the following algorithm: 1. Pick a starting point (x.y) in space. Compute the electric field vector direction there. 2. Take a small step along this vector to another point. Compute the electric field vector at this point. Connect the previous vector to this one. 3. Repeat 2. until you step off the page, step into a charge, or reach a location where the electric field is zero. 4. Repeat 1-3 until you have enough field lines to determine the field direction in a given region of the plot. 1. A point clange y is an («,y) ** (-1,0) aKi a pa ini eharge +q is at (x,y) = (+1,0) meters. Draw an electric field line for each of the following starting points. x,y)=(0,0.1)