1. | \(\dfrac{Q+q}{4 \pi r_{2}^{2}}\) | 2. | \(\dfrac{q}{4 \pi r_{1}^{2}}\) |
3. | \(\dfrac{-Q+q}{4 \pi r_{2}^{2}}\) | 4. | \(\dfrac{-q}{4 \pi r_{1}^{2}}\) |
The ratio of the electric flux linked with shell \(A\) and shell \(B\) in the diagram shown below is:
1. | \(1: 1\) | 2. | \(1: 2\) |
3. | \(1: 4\) | 4. | \(4: 2\) |
1. | be reduced to half |
2. | remain the same |
3. | be doubled |
4. | increase four times |
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. \(\frac{q}{2\varepsilon_0}\)
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
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 \(r>R\). |
Which of the following graphs shows the variation of electric field \(E\) due to a hollow spherical conductor of radius \(R\) as a function of distance from the centre of the sphere?
1. | 2. | ||
3. | 4. |
A point charge is placed at the center of the spherical Gaussian surface. The electric flux through the surface is changed if the:
1. | sphere is replaced by a cube of the same volume. |
2. | sphere is replaced by a cube of half volume. |
3. | charge is moved off-centre in the original sphere. |
4. | charge is moved just outside the original sphere. |
A square surface of side \(L\) (m) is in the plane of the paper. A uniform electric field \(\vec{E}\) (V/m), also in the plane of the paper, is limited only to the lower half of the square surface, (see figure). The electric flux in SI units associated with the surface is:
1. | \(EL^2/ ( 2ε_0 )\) | 2. | \(EL^2 / 2\) |
3. | zero | 4. | \(EL^2\) |
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. \(\frac{q}{\varepsilon_0}-\phi\)