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Dipole Moment

A slab of mat...

Question

A slab of material of dielectric constant K has the same area as the plates of a parallel plate capacitor but has a thickness (3/4)d, where d is the separation of the plates. How is the capacitance changed when the slab is inserted between the plates?

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Solution

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$b e f o r e i n s e r t i n g o f d i e l e c t i c s l a b C = \frac{ε_{0} A}{d} u \sin g t h e f o r m u l a o f c a p a c i \tan c e w h e n s o m e d i e l e t r i c i s i n s e r t e d p a r a l l e l t o p l a t e s C_{n e w} = \frac{ε_{0} A}{t - d + \frac{t}{K}} {h e r e t i s t h i c k n e s s o f d e e l e c t r i c a n d A i s a r e a} C_{n e w} = \frac{ε_{0} A}{\frac{3 d}{4} - d + \frac{3 d}{4 K}} s o a s w e c a n s e e t h a t d e n o m i n t o r p a r t d e c r e a s e s a s K > 1 h e n c e C_{n e w} > C w h i c h m e a n s t h e c a p a c i \tan c e i n c r e a s e s . R e g a r d s$

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