Q. No.A three coulomb charge moves from the point \((0,-2,-5)\) to the point \((5, 1, 2)\) in an electric field expressed as \(\vec{E}=2 x \hat{i}+3 {y}^2 \hat{j}+4 \hat{k} ~\text{N/C} .\) The work done in moving the charge is: (in J)
1. \(110\)
2. \(150\)
3. \(186\)
4. \(220\)
1. \(110\)
2. \(150\)
3. \(186\)
4. \(220\)
Subtopic: Electric Potential Energy |
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A point charge of \(10^{-8}~\text{C}\) is placed at the origin. The work done in moving a point charge \(2~\mu\text{C}\) from point \(A(4,4,2)~\text{m}\) to \(B(2,2,1)~\text{m}\) is: (in J)
\( \left ( \dfrac{1}{4\pi\varepsilon _0}=9\times 10^9~\text{in SI units} \right )\)
1. \(45\times 10^{-6}\)
2. \(0\)
3. \(30\times10^{-6}\)
4. \(15\times 10^{-6}\)
\( \left ( \dfrac{1}{4\pi\varepsilon _0}=9\times 10^9~\text{in SI units} \right )\)
1. \(45\times 10^{-6}\)
2. \(0\)
3. \(30\times10^{-6}\)
4. \(15\times 10^{-6}\)
Subtopic: Electric Potential Energy |
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Consider two identical metallic spheres of radius \(R\) each having charge \(Q\) and mass \(m\). Their centres have an initial separation of \(4R\). Both the spheres are given an initial speed of \(u\) towards each other. The minimum value of \(u\), so that they can just touch each other is:
(Take \(k=\dfrac{1}{4 \pi \varepsilon_0}\) and assume \(k Q^2>G m^2\) where \(G\) is the gravitational constant)
1. \(\sqrt{\dfrac{k Q^2}{4 m R}\left(1-\dfrac{G m^2}{k Q^2}\right)}\)
2. \(\sqrt{\dfrac{k Q^2}{4 m R}\left(1+\dfrac{G m^2}{k Q^2}\right)}\)
3. \(\sqrt{\dfrac{k Q^2}{2 m R}\left(1-\dfrac{G m^2}{k Q^2}\right)}\)
4. \(\sqrt{\dfrac{k Q^2}{2 m R}\left(1-\dfrac{G m^2}{2 k Q^2}\right)}\)
(Take \(k=\dfrac{1}{4 \pi \varepsilon_0}\) and assume \(k Q^2>G m^2\) where \(G\) is the gravitational constant)
1. \(\sqrt{\dfrac{k Q^2}{4 m R}\left(1-\dfrac{G m^2}{k Q^2}\right)}\)
2. \(\sqrt{\dfrac{k Q^2}{4 m R}\left(1+\dfrac{G m^2}{k Q^2}\right)}\)
3. \(\sqrt{\dfrac{k Q^2}{2 m R}\left(1-\dfrac{G m^2}{k Q^2}\right)}\)
4. \(\sqrt{\dfrac{k Q^2}{2 m R}\left(1-\dfrac{G m^2}{2 k Q^2}\right)}\)
Subtopic: Electric Potential Energy |
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Two charges \(7~ \mu \text{C}\) and \(-2~\mu \text{C}\) are placed at \((-9,0,0)\) cm and \((9,0,0)\) cm respectively in an external field \(E=\dfrac{A}{{r}^2}~ \hat{r}\), where \(A = 9 \times 10^{5}~\text{N/C m}^2\). Considering the potential at infinity is \(0\), the electrostatic energy of the configuration is: (in J)
1. \(1.4\)
2. \(-90.7\)
3. \(49.3\)
4. \(24.3\)
1. \(1.4\)
2. \(-90.7\)
3. \(49.3\)
4. \(24.3\)
Subtopic: Electric Potential Energy |
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Two points charges of \(1~\text{nC}\) and \(2~\text{nC}\) are placed at the two corners of equilateral triangle of side \(3~\text{cm}\). The work done is bringing a charge of \(3~\text{nC}\) from infinity to the third corner of a triangle is: (in \(\mu\text {J}\))
\(\dfrac{1}{4 \pi \varepsilon_0}=9 \times 10^9 ~\text{Nm}^2/\text{C}^2\)
1. \(2.7\)
2. \(5.4\)
3. \(3.3\)
4. \(27\)
\(\dfrac{1}{4 \pi \varepsilon_0}=9 \times 10^9 ~\text{Nm}^2/\text{C}^2\)
1. \(2.7\)
2. \(5.4\)
3. \(3.3\)
4. \(27\)
Subtopic: Electric Potential Energy |
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Two charges \(q_1\) and \(q_2\) are separated by a distance of \(30~ \text{cm}.\) A third charge \(q_3\) initially at \(C\) as shown in the figure, is moved along the circular path of radius \(40\) cm from \(C\) to \(D .\) If the difference in potential energy due to movement of \(q_3\) from \(C\) to \(D \) is given by \(\left(\dfrac{kq_3}{4 \pi \varepsilon_0} \right), ~\) the value of \(k\) is:
1. \(6q_2 \)
2. \(8q_2\)
3. \(6q_1\)
4. \(8q_1\)
1. \(6q_2 \)
2. \(8q_2\)
3. \(6q_1\)
4. \(8q_1\)
Subtopic: Electric Potential Energy |
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Two charges (both at rest initially), having a charge \(Q\) and \(-Q\) are released from the situation shown. If the kinetic energy of the system when the separation between them becomes half, is \({{1}\over{4\pi\epsilon_{0}}}{{Q^{2}}\over{nr_{0}}}.\) Then \(n=? \)
1. \(2\)
2. \(3\)
3. \(1\)
4. \(4\)
1. \(2\)
2. \(3\)
3. \(1\)
4. \(4\)
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An \(\alpha\) particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by the above two particles will be:
1. \(\sqrt 2 : 1 \)
2. \(2\sqrt 2 : 1 \)
3. \(4\sqrt 2 : 1 \)
4. \(8:1\)
1. \(\sqrt 2 : 1 \)
2. \(2\sqrt 2 : 1 \)
3. \(4\sqrt 2 : 1 \)
4. \(8:1\)
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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Two identical electric point dipoles have dipole moments \(\vec{P}_1=P\hat{i}\) and \(\vec{P}_2=-P\hat{i}\) and are held on the \(x\) axis at distance '\(a\)' from each other. When released, they move along the \(x\)-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is '\(m\)', their speed when they are infinitely far apart is:
1. \( \frac{P}{a} \sqrt{\frac{1}{\pi \varepsilon_0 m a}} \)
2. \(\frac{P}{a} \sqrt{\frac{3}{2 \pi \varepsilon_0 \mathrm{ma}}} \)
3. \(\frac{P}{a} \sqrt{\frac{1}{2 \pi \varepsilon_0 m a}} \)
4. \(\frac{P}{a} \sqrt{\frac{2}{\pi \varepsilon_0 \mathrm{ma}}}\)
Subtopic: Electric Potential Energy |
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