5. A thin rod of length ( and uniform charge per unit length A lies along...

 

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5. A thin rod of length ( and uniform charge per unit length A lies along the x axis as shown in Figure P19.22. (a) Show that the electric field at P, a distance y from the rod along its perpendicular bisector, has nox component and is given by E = 2ked sin Ooly. (b) Using your result to part (a), show that the field of a rod of infinite length is E - 2kA/y. (Suggestion: First, calculate the ficld at P due to an element of length dx, which has a charge A dx. Then, change variables from x to 0, using the relationships x = y tan 0 and dx = y sec'o d0, and integrate over 0.) li mriw ign h won 8o le dx Figure P19.22 5. A thin rod of length ( and uniform charge per unit length A lies along the x axis as shown in Figure P19.22. (a) Show that the electric field at P, a distance y from the rod along its perpendicular bisector, has nox component and is given by E = 2ked sin Ooly. (b) Using your result to part (a), show that the field of a rod of infinite length is E - 2kA/y. (Suggestion: First, calculate the ficld at P due to an element of length dx, which has a charge A dx. Then, change variables from x to 0, using the relationships x = y tan 0 and dx = y sec'o d0, and integrate over 0.) li mriw ign h won 8o le dx Figure P19.22