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Consider a cylindrical capacitor in a gravity-free, vacuum xyz coordinate space, standing vertically. The central axes of both cylindrical plates are the z-axis, with their center at the origin. The inner plate has a radius of 7.0 cm, the outer plate has a radius of 8.0 cm, and the length of the capacitor is 30.0 cm. Thus, the central axis of the capacitor is the line segment connecting the points (0, 0, -15) and (0, 0, 15). The capacitor is currently charged to 10V and disconnected from the power source. Now, a thin dielectric with a donut-shaped cross-section and a dielectric constant of 15 is to be inserted into the capacitor with its central axis aligned with the z-axis. The inner radius of the dielectric is 7.2 cm, the outer radius is 7.8 cm, and its height is 30.0 cm. At the moment when the dielectric is "halfway inserted" into the capacitor, such that its central axis is the line segment connecting (0, 0, 0) and (0, 0, 30), calculate the net electric force F (in Newtons) acting on the dielectric. Find the value of {(100/9)(F/(πε))}, where ε is the permittivity of free space. Edge effects are ignored, and the electric field exists only between the plates.
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무슨 학부 전자기학 과제같읕데, 챗지비티한테 던져주면 풀 수 있을듯? 푸는 방법은, E = 0.5 q2 / C 에서 고립계니까 Q는 일정하고, 도넛이 들어온 길이에 따라 C 가 변하니 E 가 변함. 결과적으로 도넛 들어온 길이에 따라 축전된 에너지가 변하니, F = dE dX 로 구할 수 있어. - dc App