1. | 2. | ||
3. | 4. |
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. | \(4:1\) |
Two metallic spheres of radii \(1~\text{cm}\) and \(3~\text{cm}\) are given charges of \(-1\times 10^{-2}~\text{C}\) and \(5\times 10^{-2} ~\text{C}\), respectively. If these are connected by a conducting wire, then the final charge on the bigger sphere is:
1. \(3\times 10^{-2}~ \text{C}\)
2. \(4\times 10^{-2}~\text{C}\)
3. \(1\times 10^{-2}~\text{C}\)
4. \(2\times 10^{-2}~\text{C}\)
A parallel plate capacitor has a uniform electric field \(E\) in the space between the plates. If the distance between the plates is \(d\) and the area of each plate is \(A,\) the energy stored in the capacitor is:
1. \(\frac{E^2 Ad}{\varepsilon_0}\)
2. \(\frac{1}{2}\varepsilon_0E^2 Ad\)
3. \(\varepsilon_0EAd\)
4. \(\frac{1}{2}\varepsilon_0E^2 \)
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. | \(\dfrac{U}{2}\) | 2. | \(\dfrac{U}{4}\) |
3. | \(4U\) | 4. | \(2U\) |
Two charges q1 and q2 are placed 30 cm apart, as shown in the figure. A third charge q3 is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is , where k is:
.
1. 8q2
2. 6q2
3. 8q1
4. 6q1
As per this diagram, a point charge \(+q\) is placed at the origin \(O.\) Work done in taking another point charge \(-Q\) from the point \(A,\) coordinates \((0,a),\) to another point \(B,\) coordinates \((a,0),\) along the straight path \(AB\) is:
1. | \( \left(\dfrac{-{qQ}}{4 \pi \varepsilon_0} \dfrac{1}{{a}^2}\right) \sqrt{2} {a}\) | 2. | zero |
3. | \( \left(\dfrac{qQ}{4 \pi \varepsilon_0} \dfrac{1}{{a}^2}\right) \dfrac{1}{\sqrt{2}} \) | 4. | \( \left(\dfrac{{qQ}}{4 \pi \varepsilon_0} \dfrac{1}{{a}^2}\right) \sqrt{2} {a}\) |