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Q. No.Six charges \(+q,\) \(-q,\) \(+q,\) \(-q,\) \(+q\) and \(-q\) are fixed at the corners of a hexagon of side \(d\) as shown in the figure. The work done in bringing a charge \(q_0\) to the centre of the hexagon from infinity is: (\(\varepsilon_0\text-\)permittivity of free space)
| 1. | zero | 2. | \(\dfrac{-q^2}{4\pi\varepsilon_0d}\) |
| 3. | \(\dfrac{-q^2}{4\pi\varepsilon_0d}\Big(3-\dfrac{1}{\sqrt2}\Big)\) | 4. | \(\dfrac{-q^2}{4\pi\varepsilon_0d}\Big(6-\dfrac{1}{\sqrt2}\Big)\) |
Subtopic: Electric Potential Energy |
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Level 1: 80%+
NEET - 2022
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Work done in carrying a charge \(Q\) from \(A\) to \(B\) (as shown in the figure) on a circle of the radius \(r\) with a charge \(Q\) at the centre is:
| 1. | \(\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{Q}{r}\) | 2. | \(\dfrac{Q^{2}}{4 \pi \varepsilon_{0} r}\) |
| 3. | zero | 4. | \(\dfrac{Q^{2}}{2 r}\) |
Subtopic: Electric Potential Energy |
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Level 1: 80%+
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Three protons, each having a mass \(m\) and charge \(e,\) are placed at rest at the corners of an equilateral triangle with side length \(a.\) The electrostatic potential energy of the system is: \(\left (\text{here,}~ k=\dfrac{1}{4\pi \varepsilon _{0}} \right )\)
| 1. | \(\dfrac{ke^{2}}{\varepsilon _{0}a}\) | 2. | \(\dfrac{3ke^{2}}{a}\) |
| 3. | \(\dfrac{3ke^{2}}{a^{2}}\) | 4. | \(\dfrac{ke^{2}}{a^{2}}\) |
Subtopic: Electric Potential Energy |
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Level 1: 80%+
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If \(E\) is the electric field intensity of an electrostatic field, then the electrostatic energy density is proportional to:
| 1. | \(E\) | 2. | \(E^2\) |
| 3. | \(\dfrac{1}{E^2}\) | 4. | \(E^3\) |
Subtopic: Electric Potential Energy |
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Level 1: 80%+
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Two charges and are placed 30 cm apart, as shown in the figure. A third charge 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. 8
2. 6
3. 8
4. 6
Subtopic: Electric Potential Energy |
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Two free charge particles of the same mass (\(m\)) and charge (\(q\)), separated by a distance \(r\), are released, when the charged particles reach at infinite separation, then the potential energy that is converted into kinetic energy will be: (consider at infinity potential is zero)
1. \(\dfrac{1}{2 \pi \varepsilon_{0}}\left(\dfrac{q^{2}}{r}\right)\)
2. \(\dfrac{1}{4 \pi \varepsilon_{0}}\left(\dfrac{q^{2}}{r}\right)\)
3. \(\dfrac{1}{4 \pi \varepsilon_{0}}\left(\dfrac{q^{2}}{r^2}\right)\)
4. \(\dfrac{1}{4 \pi \varepsilon_{0}}\left(\dfrac{2q^{}}{r}\right)\)
1. \(\dfrac{1}{2 \pi \varepsilon_{0}}\left(\dfrac{q^{2}}{r}\right)\)
2. \(\dfrac{1}{4 \pi \varepsilon_{0}}\left(\dfrac{q^{2}}{r}\right)\)
3. \(\dfrac{1}{4 \pi \varepsilon_{0}}\left(\dfrac{q^{2}}{r^2}\right)\)
4. \(\dfrac{1}{4 \pi \varepsilon_{0}}\left(\dfrac{2q^{}}{r}\right)\)
Subtopic: Electric Potential Energy |
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Level 2: 60%+
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A particle of mass \(0.002\) kg and charge \(1 ~\mu\text{C}\) is held at rest on a frictionless horizontal surface at a distance of \(1\) m from a fixed charge of \(1\) mC. If the particle is released, it will be repelled. The speed of the particle when it is at a distance of \(10\) m from the fixed charge will be:
| 1. | \(60\) ms–1 | 2. | \(75\) ms–1 |
| 3. | \(90\) ms–1 | 4. | \(100\) ms–1 |
Subtopic: Electric Potential Energy |
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Twenty-seven identical spherical drops of mercury are each maintained at a potential of \(10~\text{V}.\) If all these drops coalesce to form a single large spherical drop, then the potential energy of this larger drop will be how many times that of one of the smaller drops?
| 1. | \(143\) | 2. | \(243\) |
| 3. | \(348\) | 4. | \(564\) |
Subtopic: Electric Potential Energy |
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A charge \(Q=2~\mu \text{C}\) is situated at the origin of co-ordinate axis. Another charge \(5~\mu\text{C}\) on the \(x\text-\)axis at point \(A(3,0) \) is brought to point \(B(0,2) \) on \(y\text-\)axis. The work done by an external agent is:
1. \(12~\text{mJ}\)
2. \(15~\text{mJ}\)
3. \(20~\text{mJ}\)
4. \(34~\text{mJ}\)
1. \(12~\text{mJ}\)
2. \(15~\text{mJ}\)
3. \(20~\text{mJ}\)
4. \(34~\text{mJ}\)
Subtopic: Electric Potential Energy |
78%
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Q. No.
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