Q. No.Suppose the charge of a proton and an electron differ slightly. One of them is \(-e,\) the other is \((e+\Delta e).\) If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance \(d\) (much greater than atomic size) apart is zero, then \(\Delta e\) is of the order of?
(Given the mass of hydrogen \(m_h = 1.67\times 10^{-27}~\text{kg}\))
1. \(10^{-23}~\text{C}\)
2. \(10^{-37}~\text{C}\)
3. \(10^{-47}~\text{C}\)
4. \(10^{-20}~\text{C}\)
(Given the mass of hydrogen \(m_h = 1.67\times 10^{-27}~\text{kg}\))
1. \(10^{-23}~\text{C}\)
2. \(10^{-37}~\text{C}\)
3. \(10^{-47}~\text{C}\)
4. \(10^{-20}~\text{C}\)
An electron falls from rest through a vertical distance \(h\) in a uniform and vertically upward-directed electric field \(E\). The direction of the electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest through the same vertical distance \(h\). The fall time of the electron in comparison to the fall time of the proton is:
| 1. | smaller | 2. | \(5\) times greater |
| 3. | \(10\) times greater | 4. | equal |
1. \(v\propto x\)
2. \(v\propto x^{-1/2}\)
3. \(v\propto x^{-1}\)
4. \(v\propto x^{1/2}\)
The electric field in a certain region is acting radially outward and is given by \(E=Aa.\) A charge contained in a sphere of radius \(a\) centered at the origin of the field will be given by:
1. \(4 \pi \varepsilon_{{o}} {A}{a}^2\)
2. \(\varepsilon_{{o}} {A} {a}^2\)
3. \(4 \pi \varepsilon_{{o}} {A} {a}^3\)
4. \(\varepsilon_{{o}} {A}{a}^3\)
1. \(\frac{r}{\sqrt[3]{2}}\)
2. \(\frac{r}{\sqrt[2]{2}}\)
3. \(\frac{2r}{3}\)
4. none of the above
What is the flux through a cube of side \(a,\) if a point charge of \(q\) is placed at one of its corners?
1. \(\dfrac{2q}{\varepsilon_0}\)
2. \(\dfrac{q}{8\varepsilon_0}\)
3. \(\dfrac{q}{\varepsilon_0}\)
4. \(\dfrac{q}{2\varepsilon_0}\)
| 1. | be reduced to half |
| 2. | remain the same |
| 3. | be doubled |
| 4. | increase four times |
Two positive ions, each carrying a charge \(q\), are separated by a distance \(d\). If \(F\) is the force of repulsion between the ions, the number of electrons missing from each ion will be:
(\(e\) is the charge on an electron)
| 1. | \(\frac{4 \pi \varepsilon_{0} F d^{2}}{e^{2}}\) | 2. | \(\sqrt{\frac{4 \pi \varepsilon_{0} F e^{2}}{d^{2}}}\) |
| 3. | \(\sqrt{\frac{4 \pi \varepsilon_{0} F d^{2}}{e^{2}}}\) | 4. | \(\frac{4 \pi \varepsilon_{0} F d^{2}}{q^{2}}\) |
A square surface of side \(L\) (metre) in the plane of the paper is placed in a uniform electric field \(E\) (volt/m) acting along the same plane at an angle θ with the horizontal side of the square as shown in the figure. The electric flux linked to the surface in the unit of V-m is:
| 1. | \(EL^{2}\) | 2. | \(EL^{2} cos\theta \) |
| 3. | \(EL^{2} sin\theta \) | 4. | \(0\) |
A thin conducting ring of the radius \(R\) is given a charge \(+Q.\) The electric field at the centre \(O\) of the ring due to the charge on the part \(AKB\) of the ring is \(E.\) The electric field at the centre due to the charge on the part \(ACDB\) of the ring is:
| 1. | \(3E\) along \(KO\) |
| 2. | \(E\) along \(OK\) |
| 3. | \(E\) along \(KO\) |
| 4. | \(3E\) along \(OK\) |
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