A) \[Q=\frac{{{\varepsilon }_{0}}AV}{d}\]
B) \[W=\frac{{{\varepsilon }_{0}}A{{V}^{2}}}{2Kd}\]
C) \[E=\frac{{{V}^{{}}}}{Kd}\]
D) \[W=\frac{{{\varepsilon }_{0}}A{{V}^{2}}}{2d}\left( 1-\frac{1}{K} \right)\]
Correct Answer: D
Solution :
[d] After inserting the dielectric slab New capacitance \[C'=K.C=\frac{K{{\varepsilon }_{0}}A}{d}\] New potential difference \[V'=\frac{V}{K}\] New charge \[Q'=C'V'=\frac{{{\varepsilon }_{0}}AV}{d}\] Mew electric field \[E'=\frac{V'}{d}=\frac{V}{Kd}\] Work done (W) = final energy - initial energy \[W=\frac{1}{2}C'V{{'}^{2}}-\frac{1}{2}C{{V}^{2}}=\frac{1}{2}(KC){{\left( \frac{V}{K} \right)}^{2}}-\frac{1}{2}C{{V}^{2}}\] \[=\frac{1}{2}C{{V}^{2}}\left( \frac{1}{K}-1 \right)=-\frac{1}{2}C{{V}^{2}}=\left( 1-\frac{1}{K} \right)\] \[=\frac{{{\varepsilon }_{0}}A{{V}^{2}}}{2d}\left( 1-\frac{1}{K} \right)\]so \[\left| W \right|=\frac{{{\varepsilon }_{0}}A{{V}^{2}}}{2d}\left( 1-\frac{1}{K} \right)\]You need to login to perform this action.
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