A parallel-plate capacitor of width w, length L, and separation of d has a solid dielectric...

 

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A parallel-plate capacitor of width w, length L, and separation of d has a solid dielectric slab of relative permittivity of , in the space between the plates. As shown in Figure 4, the capacitor is charged to a voltage of Vo by a battery. Assuming that the dielectric slab is withdrawn to the position shown, determine the horizontal force acting on the slab. H Hint: Consider two capacitors in parallel: C with a length of and width w, and C2 with a length of L-I and width w. The total capacitance is the sum of the two capacitors: C = C +C. Find the stored energy We corresponding to the two capacitors. The stored energy is calculated using We = cv2 Finally, take the gradient of We to find the force, with a being the variable, i.e. We. Vo L Figure 4: A parallel-plate capacitor with a dielectric slab of relative permittivity of , in the s space between. A parallel-plate capacitor of width w, length L, and separation of d has a solid dielectric slab of relative permittivity of , in the space between the plates. As shown in Figure 4, the capacitor is charged to a voltage of Vo by a battery. Assuming that the dielectric slab is withdrawn to the position shown, determine the horizontal force acting on the slab. H Hint: Consider two capacitors in parallel: C with a length of and width w, and C2 with a length of L-I and width w. The total capacitance is the sum of the two capacitors: C = C +C. Find the stored energy We corresponding to the two capacitors. The stored energy is calculated using We = cv2 Finally, take the gradient of We to find the force, with a being the variable, i.e. We. Vo L Figure 4: A parallel-plate capacitor with a dielectric slab of relative permittivity of , in the s space between.