A capacitor is made of two square plates each of side $a$ making a very small angle $\alpha$ between them, as shown in figure. The capacitance will be close to
A capacitor is made of two square plates each of side $a$ making a very small angle $\alpha$ between them, as shown in figure. The capacitance will be close to
- [JEE MAIN 2020]
- A
$\frac{\varepsilon_{0} a^{2}}{d}\left(1-\frac{3 \alpha a}{2 d}\right)$
- B
$\frac{\varepsilon_{0} a^{2}}{d}\left(1-\frac{\alpha a}{4 d}\right)$
- C
$\frac{\varepsilon_{0} {a}^{2}}{\mathrm{d}}\left(1+\frac{\alpha {a}}{\mathrm{d}}\right)$
- D
$\frac{\varepsilon_{0} a^{2}}{d}\left(1-\frac{\alpha a}{2 d}\right)$
Similar Questions
We have three identical metallic spheres $A, B$ and $C$. $A$ is given a charge $Q$, and $B$ and $C$ are uncharged. The following processes of touching of two spheres are carried out in succession. Each process is carried out with sufficient time.
$(i)$ $A$ and $B$ $(ii)$ $B$ and $C$
$(iii)$ $C$ and $A$ $(iv)$ $A$ and $B$
$(v)$ $B$ and $C$
The final charges on the spheres are
We have three identical metallic spheres $A, B$ and $C$. $A$ is given a charge $Q$, and $B$ and $C$ are uncharged. The following processes of touching of two spheres are carried out in succession. Each process is carried out with sufficient time.
$(i)$ $A$ and $B$ $(ii)$ $B$ and $C$
$(iii)$ $C$ and $A$ $(iv)$ $A$ and $B$
$(v)$ $B$ and $C$
The final charges on the spheres are
Two conducting shells of radius $a$ and $b$ are connected by conducting wire as shown in figure. The capacity of system is :
Two conducting shells of radius $a$ and $b$ are connected by conducting wire as shown in figure. The capacity of system is :
A parallel-plate capacitor is connected to a resistanceless circuit with a battery until the capacitor is fully charged. The battery is then disconnected from the circuit and the plates of the capacitor are moved to half of their original separation using insulated gloves. Let $V_{new}$ be the potential difference across the capacitor plates when the plates have moved. Let $V_{old}$ be the potential difference across the capacitor plates when they were connected to the battery $\frac{V_{new}}{V_{old}}=$......
A parallel-plate capacitor is connected to a resistanceless circuit with a battery until the capacitor is fully charged. The battery is then disconnected from the circuit and the plates of the capacitor are moved to half of their original separation using insulated gloves. Let $V_{new}$ be the potential difference across the capacitor plates when the plates have moved. Let $V_{old}$ be the potential difference across the capacitor plates when they were connected to the battery $\frac{V_{new}}{V_{old}}=$......
A $500\,\mu F$ capacitor is charged at a steady rate of $100\, \mu C/sec$. The potential difference across the capacitor will be $10\, V$ after an interval of.....$sec$
A $500\,\mu F$ capacitor is charged at a steady rate of $100\, \mu C/sec$. The potential difference across the capacitor will be $10\, V$ after an interval of.....$sec$
A $500 \,\mu F$ capacitor is charged at a steady rate of $100\, \mu C/sec$. The potential difference across the capacitor will be $10\, V$ after an interval of.....$sec$
A $500 \,\mu F$ capacitor is charged at a steady rate of $100\, \mu C/sec$. The potential difference across the capacitor will be $10\, V$ after an interval of.....$sec$