Q. No.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
1. \( p^2 E\)
2. \( p E\)
3. infinite
4. \( {pE}^2\)
| 1. | \(\dfrac{-Q}{4}\) | 2. | \(\dfrac{Q}{4}\) |
| 3. | \(\dfrac{-Q}{2}\) | 4. | \(\dfrac{Q}{2}\) |
What is the flux through a cube of side \(a,\) if a point charge of \(q\) is placed at one of its corners?
1. \(\frac{2q}{\varepsilon_0}\)
2. \(\frac{q}{8\varepsilon_0}\)
3. \(\frac{q}{\varepsilon_0}\)
4. \(\frac{q}{2\varepsilon_0}\)
| 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. | \(0\) |
The electric field at a distance \(\frac{3R}{2}\) from the centre of a charged conducting spherical shell of radius \(R\) is \(E\). The electric field at a distance \(\frac{R}{2}\) from the centre of the sphere is:
1. \(E\)
2. \(\frac{E}{2}\)
3. \(\frac{E}{3}\)
4. zero
1. \(8\times 10^{7}\)
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