Two tiny spheres carrying charges of \(1.5\) µC and \(2.5\) µC are located \(30\) cm apart. What is the potential at a point \(10\) cm from the midpoint in a plane normal to the line and passing through the mid-point?
1. \(1.5\times 10^{5}\) V
2. \(1.0\times 10^{5}\) V
3. \(2.4\times 10^{5}\) V
4. \(2.0\times 10^{5}\) V
A \(12\) pF capacitor is connected to a \(50\) V battery. How much electrostatic energy is stored in the capacitor?
1. \(3.1\times10^{-8}\) J
2. \(2.9\times10^{-8}\) J
3. \(3.3\times10^{-8}\) J
4. \(1.5\times10^{-8}\) J
In a parallel plate capacitor with air between the plates, each plate has an area of \(6\times10^{-3}~\text{m}^2\), and the distance between the plates is \(3~\text{mm}\). The capacitance of the capacitor is:
1. \(16.12~\text{pF}\)
2. \(17.71~\text{pF}\)
3. \(15.01~\text{pF}\)
4. \(11.32~\text{pF}\)
Three capacitors of capacitances \(2\) pF, \(3\) pF, and \(4\) pF are connected in parallel. The charge on the \(4\) pF capacitor, if the combination is connected to a \(100\) V supply, is:
1.\(4\times10^{-10}\) C
2. \(3\times10^{-9}\) C
3. \(2\times10^{-10}\) C
4. \(1\times10^{-9}\) C
Three capacitors connected in series have a capacitance of \(9\) pF each. The potential difference across each capacitor if the combination is connected to a \(120\) V supply is:
1. \(10\) V
2. \(20\) V
3. \(30\) V
4. \(40\) V
In a certain region of space with volume \(0.2\) m3, the electric potential is found to be \(5\) V throughout. The magnitude of electric field in this region is:
1. \(0.5\) N/C
2. \(1\) N/C
3. \(5\) N/C
4. zero
Consider a uniform electric field in the \(\mathrm{z}\)-direction. The potential is a constant:
a. | in all space. |
b. | for any \(\mathrm{x}\) for a given \(\mathrm{z}.\) |
c. | for any \(\mathrm{y}\) for a given \(\mathrm{z}.\) |
d. | on the \(\mathrm{x-y}\) plane for a given \(\mathrm{z}.\) |
Choose the correct option:
1. | (c), (d) |
2. | (a), (c) |
3. | (b), (c), (d) |
4. | (a), (b) |
The electrostatic potential on the surface of a charged conducting sphere is \(100~\text{V}\). Two statements are made in this regard.
Statement I: | At any point inside the sphere, electric intensity is zero. |
Statement II: | At any point inside the sphere, the electrostatic potential is \(100~\text{V}\). |
Which of the following is a correct statement?
1. | Statement I is true but Statement II is false. |
2. | Both Statement I and Statement II are false. |
3. | Statement I is true, Statement II is also true and Statement I is the cause of Statement II. |
4. | Statement I is true, Statement II is also true but the statements are independent. |
As per this diagram, a point charge \(\mathrm{+q}\) is placed at the origin \(\mathrm{O}.\) Work done in taking another point charge \(\mathrm{-Q}\) from the point \(\mathrm{A},\) coordinates \((\mathrm{0,a}),\) to another point \(\mathrm{B},\) coordinates \((\mathrm{a,0}),\) along the straight path \(\mathrm{AB}\) is:
1. | \( \left(\frac{-\mathrm{qQ}}{4 \pi \varepsilon_0} \frac{1}{\mathrm{a}^2}\right) \sqrt{2} \mathrm{a}\) | 2. | zero |
3. | \( \left(\frac{\mathrm{qQ}}{4 \pi \varepsilon_0} \frac{1}{\mathrm{a}^2}\right) \frac{1}{\sqrt{2}} \) | 4. | \( \left(\frac{\mathrm{qQ}}{4 \pi \varepsilon_0} \frac{1}{\mathrm{a}^2}\right) \sqrt{2} \mathrm{a}\) |
Some charge is being given to a conductor. Then it's potential:
1. | is maximum at the surface. |
2. | is maximum at the centre. |
3. | remains the same throughout the conductor. |
4. | is maximum somewhere between the surface and the centre. |