Q. No.The work done to move a charge along an equipotential from A to B:
1.
can not be defined as \(-\int_{\mathrm{A}}^{\mathrm{B}} \text { E. dl. }\)
2.
must be defined as \(-\int_{\mathrm{A}}^{\mathrm{B}} \text { E. dl. }\)
3.
is zero
4.
can have a non-zero value.
In a region of constant potential:
| 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 d1 and dielectric constant K1 and the other has thickness d2 and dielectric constant K2, as shown in the figure. This arrangement can be thought of as a dielectric slab of thickness d = d1 + d2 and effective dielectric constant K. K is:
| 1. | \(\frac{\mathrm{K}_{1} \mathrm{~d}_{1}+\mathrm{K}_{2} \mathrm{~d}_{2}}{\mathrm{~d}_{1}+\mathrm{d}_{1}}\) | 2. | \(\frac{\mathrm{K}_{1} \mathrm{~d}_{1}+\mathrm{K}_{2} \mathrm{~d}_{2}}{\mathrm{~K}_{1}+\mathrm{K}_{2}}\) |
| 3. | \(\frac{\mathrm{K}_{1} \mathrm{~K}_{2}\left(\mathrm{~d}_{1}+\mathrm{d}_{2}\right)}{\mathrm{K}_{1} \mathrm{~d}_{2}+\mathrm{K}_{2} \mathrm{~d}_{1}}\) | 4. | \(\frac{2 \mathrm{~K}_{1} \mathrm{~K}_{2}}{\mathrm{~K}_{1}+\mathrm{K}_{2}}\) |
Consider a uniform electric field in the Z-direction. The potential is constant:
| a. | in all space |
| b. | for any x for a given z |
| c. | for any y for a given z |
| d. | on the x-y plane for a given z |
1. (a, b, c)
2. (a, c, d)
3. (b, c, d)
4. (c, d)
The variation of electrostatic potential with radial distance \(r\) from the centre of a positively charged metallic thin shell of radius \(R\) is given by the graph:
| 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. | \(\text{zero}\) |
The electric potential V at any point (x, y, z), all in meters in space is given by V = volt. The electric field at the point (1, 0, 2) in volt/meter, is:
| 1. | 8 along the negative X-axis |
| 2. | 8 along the positive X-axis |
| 3. | 16 along the negative X-axis |
| 4. | 16 along the positive X-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 \(-10\) volt to another point where the potential is \(\mathrm{V}\) volt, then the value of \(\mathrm{V}\) is:
1. \(5\) volt
2. \(-15\) volt
3. \(+15\) volt
4. \(+10\) volt
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 \(\mathrm{A}\) and \(\mathrm{B}\) is:
1. \(6~\mu\text{F}~\)
2. \(20~\mu\text{F} ~\)
3. \(3~\mu\text{F}~\)
4. \(10~\mu\text{F}\)
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