Question

Effect of a Metallic Slab A parallel-plate capocitor has a plate separation d and plate area A. An uncharged metallic slab of thickness a is inserted midway between the plates (b) The equivalent circuit of the device in part (a) consists of two capacitors in series, each having a plate separation (a) A parallel-plate capacitor of plate separation d partially filled with a metalic slab of (d-a) (a) Find the capacitance of the device. SOLUTION Conceptualize Figure (a) shows the metallic slab between the plates of the capacitor. Any charge that appears on one plate of the capacitor must induce a charge of equal magnitude and opposite sign on the near side of the slab as shown in figure (a) Consequently, the net charge on the slab remains zero and the electric field inside the slab is zero. Categorize The planes of charge on the metallic slab's upper and ower-dges are identical to the distribution o charges on the plates of a capอcito The metal between the slabs edges serves only to make an electrical connection between the edges. Therefore, we can model the edges of the slab as conducting planes and the bulk of the slab as a wire. As a result, the capacitor in figure (a) is equivalent to two capacitors in series, each having a plate separation Analyze (Use the following as necessary: toA, d, and a.) Use the rule for adding two capacitors in series to find the equivalent capacitance in figure (b) d as shown in figure C 1 2 -04 d-a

Answer 1