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A thin rod of length, L, is placed on the +x axis with its left end on the origin (0,0) as show in the diagram to the right. The rod has a charge +Qspread uniformly along its length. The point P is on the x axis a distance r from the origin.
a.Set up the integral to find the electric field at point P.Clearly show your steps.
b.Compute the electric field at point P.
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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 + +Electric Fields 1. A wire has been given a net positive electric charge Q evenly distributed along its length. The wire has a length of L and is located on the x-axis with its left end at the origin as drawn. Set up the integral you need to do to find the electric field at a distance d to the left of the origin. Some steps you may wish to follow are: a. Figure out the direction the electric field will have at our location x = -d. This will be the same as f b. Write the differential charge dą in terms of the charge per length and a differential length. c. ris a function of x which means we have to integrate to find the electric field. Write down r. d. Put everything together (including the vector direction) into one integral that would allow you to find the E-field. Write this in the box below. e. You are not required to complete the integral and no credit is given for completing the integral. d dE =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
- You have the same line of charge in the previous problem (with +6.00 nC of charge on it). But now you are measuring the electric field 1.5 m above the center of the rod – see image below. Predict the electric field at Point P in this diagram. Make sure to include a direction with your answer.Time left C For which of the following charge distributions would Gauss's law not be useful for calculating the electric field? a spherical shell of radius R with charge uniformly distributed over its surface O a. O b. an infinitely long cylinder of radius R with charge uniformly distributed over its surface Oc. a uniformly charged sphere of radius R an infinite planar sheet having constant surface charge density Oe a cylinder of radius R and height h with charge uniformly distributed over its surface NEXT PAGETime left C For which of the following charge distributions would Gauss's law not be useful for calculating the electric field? a spherical shell of radius R with charge uniformly distributed over its surface O a. Ob. an infinitely long cylinder of radius R with charge uniformly distributed over its surface Oc. a uniformly charged sphere of radius R d. an infinite planar sheet having constant surface charge density Oe a cylinder of radius R and height h with charge uniformly distributed over its surface NEXT PAGE
- Part A The figure(Figure 1) shows three charges at the corners of a square. Write the electric field at point P in component form. Assume that x-axis is horizontal and points to the right, and y-axis points upward. Express your answer in terms of the variables Q, L, unit vectors i, j and appropriate constants. Figure 1 of 1 *Answer should include i but not j L L 4QSolve the problem and draw and label a vector diagram in the given problem. Part 1. Two charges A (+30 µC) and B (–40 µC) are 60 cm apart. What is the net field strength at a point midway between them? Part 2. What is the net electric field intensity at a point 20 cm to the left of charge A in No.1? Assume that the point and the charges are collinear.Three point charges +q, +2q and +3q are located on 3 corners of a square as shown in the diagram to the right. a.What is the electric field at point P (the forth corner)?
- Determine the magnitude of the electric field E⃗ at the origin 0 in Figure 1 due to the two charges at A and B. Express your answer in terms of the variables Q, l, k, and appropriate constants. Determine the direction of the electric field E⃗ at the origin 0 in the figure due to the two charges at A and B. Repeat A, but let the charge at B be reversed in sign. Express your answer in terms of the variables Q, l, k, and appropriate constants. Repeat B, but let the charge at B be reversed in sign.The infinite sheets (non conducting) in the figure below are both positively charged. The sheet on the. left has uniform surface charge density of 18 PC/m², and the one on the right has a uniform surface charge density of 24.0 uC/m. a. What are the magnitude and direction of the net electric field at points A, B, and C ? b. What is the force. exerted on an electron placed at points A. B, and C?Positive charge Q is distributed uniformly along the x-axis from x=0 to x=a. A positive point charge q is located on the positive x-axis at x=a+r, a distance r to the right of the end of Q. (Figure 1) Part A Calculate the x-component of the electric field produced by the charge distribution Qat points on the positive x-axis where x>a. Express your answer in terms of the variables Q, a, x, r, and appropriate constants. Part B Calculate the y-component of the electric field produced by the charge distribution Q at points on the positive x-axis where x>a. Express your answer in terms of the variables Q, a, x, r, and appropriate constants. Part C Calculate the magnitude of the force that the charge distribution Q exerts on q. Express your answer in terms of the variables Q.Part D In what direction the charge distribution Q exerts force on q. In what direction the charge distribution exerts force on .to the left to the right