Please answer all parts and show your work, thanks.

(1'|}%} Problem 5: Aictionless device changes the gap width= and hence the capacitance. of an airlled parallelplate capacitor. A switch allows a 3:5 V voltage source to be connected to and disconnected from the capacitor. With the initial gap width, the capacitance is 738.8 pF. The switch is closed allowing the capacitor to become full},r charged. The switch is then opened, and the gap width is changed until the capacitance is 111.2 pF. E> & 25% Part (:1) Mat is the magnitude of the work, inmillijoules, that is required to change the gap width from the initial value to the nal value? Grade Summary "W = | mJ Deductions 0% Potential 100% Submissions Attempts remaining: I 4 946 per attempt) detailed View I u. A 25% Part (a) What is the magnitude of the work, in millijoules, that is required to change the gap width from the initial value to the final value? A 25% Part (b) What is the ratio of the final gap width to the initial gap width? Grade Summary d final / dinitial = Deductions 0% Potential 100% sin() cos() tanO 7 HOME Submissions cotan() asin() acos() F TA 4 5 6 Attempts remaining: 5 (4% per attempt) atan() acotan() sinh() 1 2 3 detailed view coshO tanh() cotanh() + END O Degrees O Radians NO BACKSPACE DEL CLEAR Submit Hint Feedback I give up! Hints: 1 for a 0% deduction. Hints remaining: 0 Feedback: 0% deduction per feedback. -The capacitance of a parallel-plate capacitor is inversely proportional to the gapE a 25% Part (a) 'What is the magnitude of the worlg in millij oules, that is required to change the gap width from the initial value to the final value? E a 25% Part (b) What is the ratio ofthe nal gap width to the initial gap width? E; a 25% Part (c) With the final gap width, what is the potential diEereuce, in volts, across the capacitor? Grade Summary Vnal = | V Deductions 0% Potential 100% Submissions Attempts remaining: H % per attempt) detailed View Sum Hints: i for a 0% deduction. Hints remaining: 1 Feedback: 0% deduction per feedback. -The charge ispmportional to the voltage across the capacitor, and the capacitance is the constant or proportionality. E a 25% Part (:1) Which statement best describes the work done by the electrostatic force between the plates and the external force that caused the plates to change their separation? A 25% Part (a) What is the magnitude of the work, in millijoules, that is required to change the gap width from the initial value to the final value? A 25% Part (b) What is the ratio of the final gap width to the initial gap width? A 25% Part (c) With the final gap width, what is the potential difference, in volts, across the capacitor? A 25% Part (d) Which statement best describes the work done by the electrostatic force between the plates and the external force that caused the plates to change their separation? Grade Summary O The work done by the electrostatic force is negative, but the work done by the external force is positive. Deductions 0% O The work done by both of the forces is positive. Potential 100% O The work done by the electrostatic force is positive, but the work done by the external force is negative. O The work done by both of the forces is negative. Submissions Attempts remaining: 3 (33% per attempt) detailed view Submit Hint Feedback I give up! Hints: 1 for a 0% deduction. Hints remaining: 0 Feedback: 0% deduction per feedback. Recall the the work is give by the dot product of two vectors: dW = F . ds