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1.2 Consider an infinite straight line of constant, positive charge density o (in units of C/m). 1. Using a symmetry argument, show that the electric field set up by the charge den- sity is in cylindrical coordinates of the form E(r) = E(r) e, (meaning it points away from the line and does not depend on z, nor on the angle ø). 2. Using Gauss's Law, find an expression for E(r). As volume N use a cylinder of height h and radius r, and with axis the z-axis, as shown in the picture. 3. Using the relation V (r2) – V(r1) = - E dr find an expression for the potential difference. For C, use a straight line.

1.2 Consider an infinite straight line of constant, positive charge density o (in units of C/m). 1. Using a symmetry argument, show that the electric field set up by the charge den- sity is in cylindrical coordinates of the form E(r) = E(r) e, (meaning it points away from the line and does not depend on z, nor on the angle ø). 2. Using Gauss's Law, find an expression for E(r). As volume N use a cylinder of height h and radius r, and with axis the z-axis, as shown in the picture. 3. Using the relation V (r2) – V(r1) = - E dr find an expression for the potential difference. For C, use a straight line.

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1.2 Consider an infinite straight line of constant, positive charge density o (in units of C/m). 1. Using a symmetry argument, show that the electric field set up by the charge den- sity is in cylindrical coordinates of the form E(r) = E(r) e, (meaning it points away from the line and does not depend on z, nor on the angle ø). 2. Using Gauss's Law, find an expression for E(r). As volume N use a cylinder of height h and radius r, and with axis the z-axis, as shown in the picture. 3. Using the relation V (r2) – V(r1) = - E dr find an expression for the potential difference. For C, use a straight line.
Transcribed Image Text:1.2 Consider an infinite straight line of constant, positive charge density o (in units of C/m). 1. Using a symmetry argument, show that the electric field set up by the charge den- sity is in cylindrical coordinates of the form E(r) = E(r) e, (meaning it points away from the line and does not depend on z, nor on the angle ø). 2. Using Gauss's Law, find an expression for E(r). As volume N use a cylinder of height h and radius r, and with axis the z-axis, as shown in the picture. 3. Using the relation V (r2) – V(r1) = - E dr find an expression for the potential difference. For C, use a straight line.
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