A parallel plate capacitor with cross-sectional area \(A\) and separation \(d\) has air between the plates. An insulating slab of the same area but the thickness of \(\dfrac{d}{2}\) is inserted between the plates as shown in the figure having a dielectric constant, \(K=4\). The ratio of new capacitance to its original capacitance will be:
1. | \(2:1\) | 2. | \(8:5\) |
3. | \(6:5\) | 4. | \(4:1\) |
Three charges, each \(+q\), are placed at the corners of an equilateral triangle \(ABC\) of sides \(BC\), \(AC\), and \(AB\). \(D\) and \(E\) are the mid-points of \(BC\) and \(CA\). The work done in taking a charge \(Q\) from \(D\) to \(E\) is:
1. | \(\frac{3qQ}{4\pi \varepsilon_0 a}\) | 2. | \(\frac{3qQ}{8\pi \varepsilon_0 a}\) |
3. | \(\frac{qQ}{4\pi \varepsilon_0 a}\) | 4. | \(\text{zero}\) |
1. | \(8\) along the negative \(X\text-\)axis |
2. | \(8\) along the positive \(X\text-\)axis |
3. | \(16\) along the negative \(X\text-\)axis |
4. | \(16\) along the positive \(X\text-\)axis |
1. | increase. | 2. | decrease. |
3. | remain the same. | 4. | become zero. |
1. | 2. | ||
3. | 4. |
The effective capacity of the network between terminals \(\mathrm{A}\) and \(\mathrm{B}\) is:
1. | \(6~\mu\text{F}~\) | 2. | \(20~\mu\text{F} ~\) |
3. | \(3~\mu\text{F}~\) | 4. | \(10~\mu\text{F}\) |
1. | \(40\) V | 2. | \(10\) V |
3. | \(30\) V | 4. | \(20\) V |
A bullet of mass \(2\) g is having a charge of \(2\) µC. Through what potential difference must it be accelerated, starting from rest, to acquire a speed of \(10\) m/s?
1. \(50\) kV
2. \(5\) V
3. \(50\) V
4. \(5\) kV
1. | \(q\cdot E\) and \(p\cdot E \) |
2. | zero and minimum |
3. | \(q\cdot E\) and maximum |
4. | \(2q\cdot E\) and minimum |
1. | \(6 E,6 C\) | 2. | \( E,C\) |
3. | \(\frac{E}{6},6C\) | 4. | \(E,6C\) |