Problem 4 A particle of charge q₁ is placed at the origin. A is located at x=20 m. The electric potential at A is VA = -54 V 1 2 91 A Calculate the charge of the particle: C You are asked to place another charged particle q₂ on the x-axis at a distance 'd' from the origin in a way so that the

Three point charges, Q₁ = 21.4 µC, Q2 = −38.6 µC, and Q3 = 57.3 µC, are arranged as shown in the figure. The lengths y and x both equal 80.1 cm. Calculate the electric potential V at point A. V = x10 TOOLS V Q₁ + Q2 + A Q3

Problem 5 Consider a parallel-plate capacitor with a plate area of A = 8.50 cm². The separation between the plates is d₂ = 3.00 mm (the space between the plates is filled with air). The plates of the capacitor are charged by a 6.00 V battery, i.e., the potential difference between the plates is V₂ = 6.00 V. The plates are then disconnected from the battery and pulled apart (without discharge) to a sepa- ration of df = 8.00 mm. In the following, neglecting any fringing effects. (a) Will the new potential difference between the plates be larger, smaller, or the same compared to the initial potential difference of V₂ = 6.00 V? Explain. (Hint: Note that the charge will not change when the plates are pulled apart. Why is that?) (b) Find the potential difference Vf between the plates after the plates have been pulled to their new, larger separation df. (c) Find the electrostatic energy stored in the capacitor before and after the plates are pulled apart. (d) To separate the plates, you will…

Six negative point charges and two positive point charges are arranged in a circle as shown in the figure. The charges have equal magnitude. The magnitude of the electric potential generated by each charge is 120 V at the origin. What is the net electric potential generated by all the charges at the origin O? 90 y -Q Fig. A Answer: Net potential Answer: Net potential Volts Volts

Consider two separate systems with four charges of the same magnitude q = 16 µC arranged in the vertexes of a square of length h = 35 cm, see the picture below. Calculate the electric potential at the center of the square (points A and C) and at the middle of the bottom side of the square (points B and D). h A. C. h B D -4 The potential at point A, VA = 2324567.7 x Units V The potential at point B, Ve = 2378380.6 Units V The potential at point C, Vc =0 Units V The potential at point D, V, = -908380.8: v Units v How much work is required to move a -12 µC charge from point A to point B? The work required, W = -0.64575 xUnits J How much work is required to move a -12 µC charge from point C to point D? Units J The work required, Wc-p = 10.90

A solid aluminum sphere with radius a has an explicitly negative charge,−q. Concentric with the aluminum sphere is a copper spherical shell with inner radius b, outer radius c, and an explicitly positive charge, +Q. Assume that the magnitude of the positive charge on the copper shell is greater than the magnitude of the negative charge on the aluminum sphere, and take the electric potential at infinity as zero. Enter an expression for the electric potential, V, that is valid for a