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A certain amount of excess charge is transferred a conducting sphere with a diameter of 30 cm such that the electric potential at the center of the sphere is equal to 2.5 kV. a. How much charge was transferred to the conducting sphere? b. Determine the electric potential at a point outside of the sphere with a distance of 5 cm from its surface. c. Determine the charge density of the sphere. (Hint: surface or volume?)

A certain amount of excess charge is transferred a conducting sphere with a diameter of 30 cm such that the electric potential at the center of the sphere is equal to 2.5 kV. a. How much charge was transferred to the conducting sphere? b. Determine the electric potential at a point outside of the sphere with a distance of 5 cm from its surface. c. Determine the charge density of the sphere. (Hint: surface or volume?)

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Show your complete solution to each problem on a short bond paper. Answers must be expressed in engineering notation (when the exponent of the base 10 multiplier is not a multiple of 3, press ENG or SHIFT+ENG, whichever the case.) Example: 0.06N or 6.0x10-2 N must be expressed to 60x10-3 N or 60mN 1. Two point charges q1 = +26µC and q2 = -17.5µC are 64 cm apart. a. What is the potential energy of the system of two charges? b. What is the electric potential at a point between them 24 cm from q1? 2. Three point charges q, = +2.7µC, q2 = -3.4µC and q3 = -1.6µC initially are infinitely far apart. They are then brought together and placed at the corners of an equilateral triangle. Each side has a length of 40 cm. Determine the total electric potential energy of these group of charges. 3. Two point charges q; = 2.2nC and q2 = -1.5nC are 13 cm apart. Point A is midway between the charges and point B is 12 cm from q1 and 5 cm from q2. Calculate: a. the electric potential at point A and at point B b. the work done by the electric field on a charge of q3 = +3.6nC that moves from A to B 4. A certain amount of excess charge is transferred a conducting sphere with a diameter of 30 cm such that the electric potential at the center of the sphere is equal to 2.5 kV. a. How much charge was transferred to the conducting sphere? b. Determine the electric potential at a point outside of the sphere with a distance of 5 cm from its surface. c. Determine the charge density of the sphere. (Hint: surface or volume?) 5. At a corner of a 30 mm x 40 mm rectangle is placed a charge of -40µC and at the two adjacent corners are charges of +20µC, as shown in the figure. Determine: a. The potential at the 4" corner P. b. The potential at the center of the rectangle. c. The work that must be done by an external force to bring a charge q1 = +5µC from the center of the rectangle to the 4h corner P. 91 = +20 µC 92 = -40 µC B 30 mm P 40 mm 43 = +20 µC
Transcribed Image Text:Show your complete solution to each problem on a short bond paper. Answers must be expressed in engineering notation (when the exponent of the base 10 multiplier is not a multiple of 3, press ENG or SHIFT+ENG, whichever the case.) Example: 0.06N or 6.0x10-2 N must be expressed to 60x10-3 N or 60mN 1. Two point charges q1 = +26µC and q2 = -17.5µC are 64 cm apart. a. What is the potential energy of the system of two charges? b. What is the electric potential at a point between them 24 cm from q1? 2. Three point charges q, = +2.7µC, q2 = -3.4µC and q3 = -1.6µC initially are infinitely far apart. They are then brought together and placed at the corners of an equilateral triangle. Each side has a length of 40 cm. Determine the total electric potential energy of these group of charges. 3. Two point charges q; = 2.2nC and q2 = -1.5nC are 13 cm apart. Point A is midway between the charges and point B is 12 cm from q1 and 5 cm from q2. Calculate: a. the electric potential at point A and at point B b. the work done by the electric field on a charge of q3 = +3.6nC that moves from A to B 4. A certain amount of excess charge is transferred a conducting sphere with a diameter of 30 cm such that the electric potential at the center of the sphere is equal to 2.5 kV. a. How much charge was transferred to the conducting sphere? b. Determine the electric potential at a point outside of the sphere with a distance of 5 cm from its surface. c. Determine the charge density of the sphere. (Hint: surface or volume?) 5. At a corner of a 30 mm x 40 mm rectangle is placed a charge of -40µC and at the two adjacent corners are charges of +20µC, as shown in the figure. Determine: a. The potential at the 4" corner P. b. The potential at the center of the rectangle. c. The work that must be done by an external force to bring a charge q1 = +5µC from the center of the rectangle to the 4h corner P. 91 = +20 µC 92 = -40 µC B 30 mm P 40 mm 43 = +20 µC
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