Two square plates of side ‘a’ are arranged as shown in the figure. The minimum separation between plates is ‘d’ and one of the plate is inclined at small angle α with plane parallel to another plate. The capacitance of capacitor is (given$$ α is very $$small)

Question

Two square plates of side ‘a’ are arranged as shown in the figure. The minimum separation between plates is ‘d’ and one of the plate is inclined at small angle α  with plane parallel to another plate. The capacitance of capacitor is (given$$ α is very $$small)

Infinity Learn · Accepted Answer

For small strip of width dx  and separation $$d+$$αx , differential capacitance can be given $$asdC=$$∈$$0adxd+$$αx All such strips are in parallel, so we will integrate the equation C.$$=$$∈$$0a$$α$$Ind+$$α$$x0a$$ $$=$$∈$$0a$$α$$In1+$$αad  Use, $$In1+x$$ ≃ x $$-$$ $$x22$$ (for$$ small values of $$x) ≈∈$$0a$$αα$$ad-$$α$$2a22d2$$ ≈∈$$0a2d1$$−α$$a2d$$

Two square plates of side ‘a’ are arranged as shown in the figure. The minimum separation between plates is ‘d’ and one of the plate is inclined at small angle $α$ with plane parallel to another plate. The capacitance of capacitor is (given $α$ is very small)

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Two square plates of side ‘a’ are arranged as shown in the figure. The minimum separation between plates is ‘d’ and one of the plate is inclined at small angle α with plane parallel to another plate. The capacitance of capacitor is (given α is very small)

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Two square plates of side ‘a’ are arranged as shown in the figure. The minimum separation between plates is ‘d’ and one of the plate is inclined at small angle $α$ with plane parallel to another plate. The capacitance of capacitor is (given $α$ is very small)