1*. Consider the following vector fields: = 2xyzj + xyk = y + x + f...

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1*. Consider the following vector fields: = 2xyzj + xyk = y + x + f (z)k where f(2) is an arbitrary function of z E = osin 0 + cos 00 + Determine which ones could be electrostatic fields and determine the corresponding charge density. 2. Point charges q = 9, 92 = 29, and 93 = -3q where q = 2 10-3C are placed at the corners of an equilateral triangle with side length L = 0.5m as shown below: L L 3q 2q L a) What is the total electrostatic potential energy of this system? b) What is the potential energy of the charge q? c) What is the electric potential at the center of the triangle? 3. Three point charges 91, 92, and q3 are located at the corners of a rectangle with side lengths 0.6 m and 0.8 m. We know that q = 2 10-10 C and q3 = -4 10-10 C but q2 is unknown. If the total electric potential at the empty corner is zero, what is q? 0.6 m (91) 92 (93) 0.8 m 1*. Consider the following vector fields: = 2xyzj + xyk = y + x + f (z)k where f(2) is an arbitrary function of z E = osin 0 + cos 00 + Determine which ones could be electrostatic fields and determine the corresponding charge density. 2. Point charges q = 9, 92 = 29, and 93 = -3q where q = 2 10-3C are placed at the corners of an equilateral triangle with side length L = 0.5m as shown below: L L 3q 2q L a) What is the total electrostatic potential energy of this system? b) What is the potential energy of the charge q? c) What is the electric potential at the center of the triangle? 3. Three point charges 91, 92, and q3 are located at the corners of a rectangle with side lengths 0.6 m and 0.8 m. We know that q = 2 10-10 C and q3 = -4 10-10 C but q2 is unknown. If the total electric potential at the empty corner is zero, what is q? 0.6 m (91) 92 (93) 0.8 m