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3. A uniformly positively charged rod has length I and total charge Q. (a) Show that the electric potential at the point P on the y-axis is given by: P Vp = kIn (+ Va² + 1² a (Hint: Solve this problem by first considering the electric field dVp at P due to a small segment dx of the rod, which contains charge dq = Adx. Then find the net potential by integrating dVp over the length of the rod.) a dq x- (b) If the charge on the rod is 50.0µC, use l = 1.00 m and a = 10 cm to calculate the magnitude of the electric potential at point P. (c) If the charge on the rod is 50.0µC, use l = 1.00 m and a = 20 cm to calculate the magnitude of the electric potential at point Q that is above point P.

3. A uniformly positively charged rod has length I and total charge Q. (a) Show that the electric potential at the point P on the y-axis is given by: P Vp = kIn (+ Va² + 1² a (Hint: Solve this problem by first considering the electric field dVp at P due to a small segment dx of the rod, which contains charge dq = Adx. Then find the net potential by integrating dVp over the length of the rod.) a dq x- (b) If the charge on the rod is 50.0µC, use l = 1.00 m and a = 10 cm to calculate the magnitude of the electric potential at point P. (c) If the charge on the rod is 50.0µC, use l = 1.00 m and a = 20 cm to calculate the magnitude of the electric potential at point Q that is above point P.

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3. A uniformly positively charged rod has length I and total charge Q. (a) Show that the electric potential at the point P on the y-axis is given by: P Vp = kIn (+ Va² + 1² a (Hint: Solve this problem by first considering the electric field dVp at P due to a small segment dx of the rod, which contains charge dq = Adx. Then find the net potential by integrating dVp over the length of the rod.) a dq x- (b) If the charge on the rod is 50.0µC, use l = 1.00 m and a = 10 cm to calculate the magnitude of the electric potential at point P. (c) If the charge on the rod is 50.0µC, use l = 1.00 m and a = 20 cm to calculate the magnitude of the electric potential at point Q that is above point P.
Transcribed Image Text:3. A uniformly positively charged rod has length I and total charge Q. (a) Show that the electric potential at the point P on the y-axis is given by: P Vp = kIn (+ Va² + 1² a (Hint: Solve this problem by first considering the electric field dVp at P due to a small segment dx of the rod, which contains charge dq = Adx. Then find the net potential by integrating dVp over the length of the rod.) a dq x- (b) If the charge on the rod is 50.0µC, use l = 1.00 m and a = 10 cm to calculate the magnitude of the electric potential at point P. (c) If the charge on the rod is 50.0µC, use l = 1.00 m and a = 20 cm to calculate the magnitude of the electric potential at point Q that is above point P.
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