A toy car with charge \(q\) moves on a frictionless horizontal plane surface under the influence of a uniform electric field \(\vec E.\)Due to the force \(q\vec E,\) its velocity increases from \(0\) to \(6~\text{m/s}\) in a one-second duration. At that instant, the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between \(0\) to \(3\) seconds are respectively:
1. \(2~\text{m/s}, ~4~\text{m/s}\)
2. \(1~\text{m/s}, ~3~\text{m/s}\)
3. \(1~\text{m/s}, ~3.5~\text{m/s}\)
4. \(1.5~\text{m/s},~ 3~\text{m/s}\)
The electric field in a certain region is acting radially outward and is given by \(E=Ar.\) 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. \(\varepsilon_{{o}} {A}{a}^3\)
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. \(\sqrt{\frac{4 \pi \varepsilon_{0} F d^{2}}{d^{2}}}\)
3. \(\sqrt{\frac{4 \pi \varepsilon_{0} F d^{2}}{e^{2}}}\)
4. \(\frac{4 \pi \varepsilon_{0} F d^{2}}{q^{2}}\)
A thin conducting ring of radius \(R\) is given a charge \(+Q.\) The electric field at the centre \(\text{O}\) 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
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 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. \(\frac{q}{\varepsilon_0}-\phi\)
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. | \(EL^2\) |
Two point charges \(A\) and \(B\), having charges \(+Q\) and \(-Q\) respectively, are placed at a certain distance apart and the force acting between them is \(F.\) If \(25\%\) charge of \(A\) is transferred to \(B\), then the force between the charges becomes:
1. | \(\frac{4F}{3}\) | 2. | \(F\) |
3. | \(\frac{9F}{16}\) | 4. | \(\frac{16F}{9}\) |