Q. No.Three charges, each \(+q\), are placed at the corners of an equilateral triangle \(ABC\) of sides \(BC\), \(AC\), and \(AB\). \(D\) and \(E\) are the mid-points of \(BC\) and \(CA\). The work done in taking a charge \(Q\) from \(D\) to \(E\) is:
1.
\(\frac{3qQ}{4\pi \varepsilon_0 a}\)
2.
\(\frac{3qQ}{8\pi \varepsilon_0 a}\)
3.
\(\frac{qQ}{4\pi \varepsilon_0 a}\)
4.
\(\text{zero}\)
| 1. | \(8~\text{V/m},\) along the negative \(x\text-\)axis |
| 2. | \(8~\text{V/m},\) along the positive \(x\text-\)axis |
| 3. | \(16~\text{V/m},\) along the negative \(x\text-\)axis |
| 4. | \(16~\text{V/m},\) along the positive \(x\text-\)axis |
As per this diagram, a point charge \(+q\) is placed at the origin \(O.\) Work done in taking another point charge \(-Q\) from the point \(A,\) coordinates \((0,a),\) to another point \(B,\) coordinates \((a,0),\) along the straight path \(AB\) is:
| 1. | \( \left(\dfrac{-{qQ}}{4 \pi \varepsilon_0} \dfrac{1}{{a}^2}\right) \sqrt{2} {a}\) | 2. | zero |
| 3. | \( \left(\dfrac{qQ}{4 \pi \varepsilon_0} \dfrac{1}{{a}^2}\right) \dfrac{1}{\sqrt{2}} \) | 4. | \( \left(\dfrac{{qQ}}{4 \pi \varepsilon_0} \dfrac{1}{{a}^2}\right) \sqrt{2} {a}\) |
| 1. | \(40\) V | 2. | \(10\) V |
| 3. | \(30\) V | 4. | \(20\) V |
A bullet of mass \(2~\text {gm}\) has a charge of \(2~\mu\text{C}.\) Through what potential difference must it be accelerated, starting from rest, to acquire a speed of \(10~\text{m/s}?\)
1. \(50~\text {kV}\)
2. \(5~\text {V}\)
3. \(50~\text {V}\)
4. \(5~\text {kV}\)
Some charge is being given to a conductor. Then it's potential:
| 1. | is maximum at the surface. |
| 2. | is maximum at the centre. |
| 3. | remains the same throughout the conductor. |
| 4. | is maximum somewhere between the surface and the centre. |
A parallel plate capacitor has a uniform electric field \(\vec{E}\) in the space between the plates. If the distance between the plates is \(d\) and the area of each plate is \(A\) the energy stored in the capacitor is:
\(\left ( \varepsilon_{0} = \text{permittivity of free space} \right )\)
1. \(\frac{1}{2}\varepsilon_0 E^2 Ad\)
2. \(\frac{E^2 Ad}{\varepsilon_0}\)
3. \(\frac{1}{2}\varepsilon_0 E^2 \)
4. \(\varepsilon_0 EAd\)
| a. | in all space |
| b. | for any \(x\) for a given \(z\) |
| c. | for any \(y\) for a given \(z\) |
| d. | on the \(x\text-y\) plane for a given \(z\) |
| 1. | (a), (b), (c) | 2. | (a), (c), (d) |
| 3. | (b), (c), (d) | 4. | (c), (d) |
| 1. | can not be defined as \(-\int_{A}^{B} { \vec E\cdot \vec{dl}}\) |
| 2. | must be defined as \(-\int_{A}^{B} {\vec E\cdot \vec{dl}}\) |
| 3. | is zero |
| 4. | can have a non-zero value. |
A thin, metallic spherical shell contains a charge \(\mathrm{Q}\) on it. A point charge \(\mathrm{q}\) is placed at the centre of the shell and another charge \(\mathrm{q}_1\) is placed outside as it is shown in the figure. All the three charges are positive. The force on the charge at the centre is:
1. towards left
2. towards right
3. upward
4. zero
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