Q. No.A spherical conductor of radius \(10~\text{cm}\) has a charge of \(3.2 \times 10^{-7}~\text{C}\) distributed uniformly. What is the magnitude of the electric field at a point \(15~\text{cm}\) from the centre of the sphere?
\(\left(\frac{1}{4\pi \varepsilon _0} = 9\times 10^9~\text{N-m}^2/\text{C}^2\right)\)
1. \(1.28\times 10^{5}~\text{N/C}\)
2. \(1.28\times 10^{6}~\text{N/C}\)
3. \(1.28\times 10^{7}~\text{N/C}\)
4. \(1.28\times 10^{4}~\text{N/C}\)
\(\left(\frac{1}{4\pi \varepsilon _0} = 9\times 10^9~\text{N-m}^2/\text{C}^2\right)\)
1. \(1.28\times 10^{5}~\text{N/C}\)
2. \(1.28\times 10^{6}~\text{N/C}\)
3. \(1.28\times 10^{7}~\text{N/C}\)
4. \(1.28\times 10^{4}~\text{N/C}\)
(\(r\gg\) separation of two charges forming the dipole, \(\varepsilon_{0} =\) permittivity of free space)
1. \(\overrightarrow{E}=\dfrac{\overrightarrow{P}}{4\pi \varepsilon _{0}r^{3}}\)
2. \(\overrightarrow{E}=\dfrac{2\overrightarrow{P}}{\pi \varepsilon _{0}r^{3}}\)
3. \(\overrightarrow{E}=-\dfrac{\overrightarrow{P}}{4\pi \varepsilon _{0}r^{2}}\)
4. \(\overrightarrow{E}=-\dfrac{\overrightarrow{P}}{4\pi \varepsilon _{0}r^{3}}\)
The acceleration of an electron due to the mutual attraction between the electron and a proton when they are \(1.6~\mathring{A}\) apart is:
\(\left(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9~ \text{Nm}^2 \text{C}^{-2}\right)\)
| 1. | \( 10^{24} ~\text{m/s}^2\) | 2 | \( 10^{23} ~\text{m/s}^2\) |
| 3. | \( 10^{22}~\text{m/s}^2\) | 4. | \( 10^{25} ~\text{m/s}^2\) |
A sphere encloses an electric dipole with charges \(\pm3\times10^{-6}~\text C.\) What is the total electric flux through the sphere?
1. \(-3\times10^{-6}~\text{N-m}^2/\text C\)
2. zero
3. \(3\times10^{-6}~\text{N-m}^2/\text C\)
4. \(6\times10^{-6}~\text{N-m}^2/\text C\)
Two parallel infinite line charges with linear charge densities \(+\lambda~\text{C/m}\) and \(+\lambda~\text{C/m}\) are placed at a distance \({R}.\) The electric field mid-way between the two line charges is:
| 1. | \(\frac{\lambda}{2 \pi \varepsilon_0 {R}}~\text{N/C}\) | 2. | zero |
| 3. | \(\frac{2\lambda}{ \pi \varepsilon_0 {R}} ~\text{N/C}\) | 4. | \(\frac{\lambda}{ \pi \varepsilon_0 {R}}~\text{N/C}\) |
| 1. | \(\frac{4F}{3}\) | 2. | \(F\) |
| 3. | \(\frac{9F}{16}\) | 4. | \(\frac{16F}{9}\) |
A hollow metal sphere of radius \(R\) is uniformly charged. The electric field due to the sphere at a distance \(r\) from the centre:
| 1. | decreases as \(r\) increases for \(r<R\) and for \(r>R\). |
| 2. | increases as \(r\) increases for \(r<R\) and for \(r>R\). |
| 3. | is zero as \(r\) increases for \(r<R\), decreases as \(r\) increases for \(r>R\). |
| 4. | is zero as \(r\) increases for \(r<R\), increases as \(r\) increases for \(r>R\). |
A hollow cylinder has a charge \(q\) coulomb within it (at the geometrical centre). If \(\phi\) is the electric flux in units of Volt-meter associated with the curved surface \(B,\) the flux linked with the plane surface \(A\) in units of volt-meter will be:
1. \(\frac{1}{2}\left(\frac{q}{\varepsilon_0}-\phi\right)\)
2. \(\frac{q}{2\varepsilon_0}\)
3. \(\frac{\phi}{3}\)
4. \(\frac{q}{\varepsilon_0}-\phi\)
Three-point charges \(+q\), \(-2q\) and \(+q\) are placed at points \((x=0,y=a,z=0)\), \((x=0, y=0,z=0)\) and \((x=a, y=0, z=0)\), respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are:
| 1. | \(\sqrt{2}qa\) along \(+y\) direction |
| 2. | \(\sqrt{2}qa\) along the line joining points \((x=0,y=0,z=0)\) and \((x=a,y=a,z=0)\) |
| 3. | \(qa\) along the line joining points \((x=0,y=0,z=0)\) and \((x=a,y=a,z=0)\) |
| 4. | \(\sqrt{2}qa\) along \(+x\) direction |
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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