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6. Write an expression for the linear charge density of the plastic rod. Use the Greek letter lambda: A.

6. Write an expression for the linear charge density of the plastic rod. Use the Greek letter lambda: A.

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A short, charged, thin, plastic rod of length 2a is placed on the y-axis. The total charge on the rod is +Q Coulombs. We want to determine the total electric field at a general point, P located on the z-axis. Notice the symmetry of the source, charged object about the z-axis. +a - a y P I 1. Is this a one or two dimensional, source-charge integration? 2. What will be the coordinate that serves as the integration variable? 3. What should we expect the y-component of the total electric field at point P to be? 4. What is the position vector for the field point, P? 5. What is the position vector for a differential element of the source charge distribution? This differential element of charge is labeled dq. 6. Write an expression for the linear charge density of the plastic rod. Use the Greek letter lambda: 1. 7. Express dq in terms of the linear charge density and the differential of the integration variable. Then, re-express it in terms of the total charge on the rod and length of the rod. 8. On the diagram, draw the displacement vector, R, that goes from dq to the field point. 9. Write the displacement vector in terms of r and y coordinates and unit vectors.
Transcribed Image Text:A short, charged, thin, plastic rod of length 2a is placed on the y-axis. The total charge on the rod is +Q Coulombs. We want to determine the total electric field at a general point, P located on the z-axis. Notice the symmetry of the source, charged object about the z-axis. +a - a y P I 1. Is this a one or two dimensional, source-charge integration? 2. What will be the coordinate that serves as the integration variable? 3. What should we expect the y-component of the total electric field at point P to be? 4. What is the position vector for the field point, P? 5. What is the position vector for a differential element of the source charge distribution? This differential element of charge is labeled dq. 6. Write an expression for the linear charge density of the plastic rod. Use the Greek letter lambda: 1. 7. Express dq in terms of the linear charge density and the differential of the integration variable. Then, re-express it in terms of the total charge on the rod and length of the rod. 8. On the diagram, draw the displacement vector, R, that goes from dq to the field point. 9. Write the displacement vector in terms of r and y coordinates and unit vectors.
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