Q. No.The work done to move a charge along an equipotential from \(A\) to \(B\):
1.
can not be defined as \(-\int_{A}^{B} { \vec E\cdot \vec{dl}}\)
2.
must be defined as \(-\int_{A}^{B} {\vec E\cdot \vec{dl}}\)
3.
is zero
4.
can have a non-zero value.
| (a) | the electric field is uniform |
| (b) | the electric field is zero |
| (c) | there can be no charge inside the region |
| (d) | the electric field shall necessarily change if a charge is placed outside the region |
Choose the correct statement(s):
| 1. | (b) and (c) | 2. | (a) and (c) |
| 3. | (b) and (d) | 4. | (c) and (d) |
A parallel plate capacitor is made of two dielectric blocks in series. One of the blocks has thickness \(d_1\) and dielectric constant \(K_1\) and the other has thickness \(d_2\) and dielectric constant \(K_2\), as shown in the figure. This arrangement can be thought of as a dielectric slab of thickness \(d= d_1+d_2\) and effective dielectric constant \(K\). The \(K\) is:
| 1. | \(\dfrac{{K}_{1} {d}_{1}+{K}_{2} {d}_{2}}{{d}_{1}+{d}_{1}}\) | 2. | \(\dfrac{{K}_{1} {d}_{1}+{K}_{2} {d}_{2}}{{K}_{1}+{K}_{2}}\) |
| 3. | \(\dfrac{{K}_{1} {K}_{2}\left({d}_{1}+{d}_{2}\right)}{{K}_{1} {d}_{2}+{K}_{2} {d}_{1}}\) | 4. | \(\dfrac{2 {K}_{1} {K}_{2}}{{K}_{1}+{K}_{2}}\) |
| a. | in all space |
| b. | for any \(x\) for a given \(z\) |
| c. | for any \(y\) for a given \(z\) |
| d. | on the \(x\text-y\) plane for a given \(z\) |
| 1. | (a), (b), (c) | 2. | (a), (c), (d) |
| 3. | (b), (c), (d) | 4. | (c), (d) |
| 1. |  |
2. |  |
| 3. |  |
4. |  |
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. | \(8~\text{V/m},\) along the negative \(x\text-\)axis |
| 2. | \(8~\text{V/m},\) along the positive \(x\text-\)axis |
| 3. | \(16~\text{V/m},\) along the negative \(x\text-\)axis |
| 4. | \(16~\text{V/m},\) along the positive \(x\text-\)axis |
If \(50~\text{J}\) of work must be done to move an electric charge of \(2~\text{C}\) from a point where the potential is \(-10~\text {volts}\) to another point where the potential is \(\text{V volts}\), then the value of \(\mathrm{V}\) is:
1. \(5~\text {volts}\)
2. \(-15~\text {volts}\)
3. \(+15~\text {volts}\)
4. \(+10~\text {volts}\)
What is the area of the plates of a \(2~\text{F}\) parallel plate capacitor, given that the separation between the plates is \(0.5~\text{cm}\)?
1. \(1100~\text{km}^2\)
2. \(1130~\text{km}^2\)
3. \(1110~\text{km}^2\)
4. \(1105~\text{km}^2\)
The effective capacity of the network between terminals \({A}\) and \(B\) is:
| 1. | \(6~\mu\text{F}\) | 2. | \(20~\mu\text{F}\) |
| 3. | \(3~\mu\text{F}\) | 4. | \(10~\mu\text{F}\) |
© 2026 GoodEd Technologies Pvt. Ltd.