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Q. No.A charge \(q\) is placed at the centre of the line joining two equal positive charges \(Q.\) The system of the three charges will be in equilibrium, if \(q\) is equal to:
1.
\(\dfrac{-Q}{4}\)
2.
\(\dfrac{Q}{4}\)
3.
\(\dfrac{-Q}{2}\)
4.
\(\dfrac{Q}{2}\)
Subtopic: Coulomb's Law |
66%
Level 2: 60%+
NEET - 2013
Hints
If \(\oint_s \vec{E} \cdot {d \vec S}=0\) over a surface, then:
| 1. | the electric field inside the surface is necessarily uniform. |
| 2. | the number of flux lines entering the surface must be equal to the number of flux lines leaving it. |
| 3. | the magnitude of electric field on the surface is constant. |
| 4. | all the charges must necessarily be inside the surface. |
Subtopic: Gauss's Law |
82%
Level 1: 80%+
NEET - 2023
Hints
Three charged particles having charges equal to \(+1~\text C,\) \(-2~\text C\) and \(+3~\text C\) are placed on the \(x\text-\)axis at \(x=1~\text{cm},\) \(2~\text{cm},\) \(3~\text{cm}\) respectively. Consider a sphere of radius \(10~\text{cm}\) centred at the origin. The magnitude of the flux of the electric field of these charges through the sphere is, numerically:
| 1. | slightly greater than \(\dfrac{2}{\varepsilon_0}\) |
| 2. | slightly less than \(\dfrac{2}{\varepsilon_0}\) |
| 3. | exactly equal to \(\dfrac{2}{\varepsilon_0}\) |
| 4. | exactly equal to \(-\dfrac{2}{\varepsilon_0}\) |
Subtopic: Gauss's Law |
80%
Level 1: 80%+
Hints
The electric field, at the centre of a square with charges placed at its four vertices as shown in the figure, is: \(\left(k=\dfrac{1}{4\pi\varepsilon_0}\right)\)
| 1. | zero | 2. | \(4\dfrac{kq}{a^2}\) |
| 3. | \(2\dfrac{kq}{a^2}\) | 4. | \(2\sqrt2\dfrac{kq}{a^2}\) |
Subtopic: Electric Field |
69%
Level 2: 60%+
Hints
Two point charges \({-q}\) and \({+q}\) are placed at a distance of \({L},\) as shown in the figure.
The magnitude of electric field intensity at a distance \({R}~(R \gg L )\) varies as:
The magnitude of electric field intensity at a distance \({R}~(R \gg L )\) varies as:
| 1. | \(\dfrac{1}{{R}^{6}}\) | 2. | \(\dfrac{1}{{R}^{2}}\) |
| 3. | \(\dfrac{1}{{R}^{3}}\) | 4. | \(\dfrac{1}{{R}^{4}}\) |
Subtopic: Electric Dipole |
71%
Level 2: 60%+
NEET - 2022
Hints
Four charges \(q,q\) and \(-q,-q\) are placed at the four vertices of a square of side \(a,\) with like charges across a diagonal. The electric field at the centre of the square is:
\(\left(k=\dfrac{1}{4\pi\varepsilon_0}\right)\)
1. zero
2. \(\sqrt2\dfrac{kq}{a^2}\)
3. \(2\dfrac{kq}{a^2}\)
4. \(4\dfrac{kq}{a^2}\)
\(\left(k=\dfrac{1}{4\pi\varepsilon_0}\right)\)
1. zero
2. \(\sqrt2\dfrac{kq}{a^2}\)
3. \(2\dfrac{kq}{a^2}\)
4. \(4\dfrac{kq}{a^2}\)
Subtopic: Electric Field |
80%
Level 1: 80%+
Hints
Equal and opposite charges are placed at the two vertices of an equilateral triangle, giving a dipole moment \(p.\) A small dipole \(p'\) is placed at the third vertex, parallel to the previous dipole. If the electric fields due to both dipoles \(p,~p',\) at the mid-point of the dipole \(p,\) are equal, then \(\dfrac{p'}{p}\) equals:
| 1. | \(3\sqrt3\) | 2. | \(\dfrac{3\sqrt3}{2}\) |
| 3. | \(\sqrt3\) | 4. | \(\dfrac{\sqrt3}{2}\) |
Subtopic: Electric Dipole |
Level 3: 35%-60%
Hints
Which of the following field configurations is/are possible?
Note: \(A,B,C\) are conductors. Other charges may be present in the vicinity.
Note: \(A,B,C\) are conductors. Other charges may be present in the vicinity.
| 1. | I, III | 2. | II |
| 3. | I, II, III | 4. | none of I, II, III |
Subtopic: Electric Field |
Level 3: 35%-60%
Hints
Identical point charges (\(q\) each), are placed at the eight corners of a cube of side \(a.\) When one of the charges is removed, the electric field at the center becomes \(E_c.\)
Now, identical point charges (same magnitude \(q\) each), are placed at the four corners of a square of side \(a.\) When one of the charges is removed, the electric field at the center becomes \(E_s.\) Then,
Now, identical point charges (same magnitude \(q\) each), are placed at the four corners of a square of side \(a.\) When one of the charges is removed, the electric field at the center becomes \(E_s.\) Then,
| 1. | \(\dfrac{E_s}{2}=\dfrac{E_C}{3}\) | 2. | \(\dfrac{E_s}{3}=\dfrac{E_C}{2}\) |
| 3. | \(\dfrac{E_s}{\sqrt2}=\dfrac{E_C}{\sqrt3}\) | 4. | \(\dfrac{E_s}{\sqrt3}=\dfrac{E_C}{\sqrt2}\) |
Subtopic: Electric Field |
62%
Level 2: 60%+
Hints
Three charges \(q,~q,~-q\) are placed at the three corners of an equilateral triangle \(ABC\), of side \(a.\)
The mid-point of side \(AB\) is \(P\) while the circumcenter of \(ABC\) is \(O\). Let the electric field at \(P\) be \(E_p\) and that at \(O\) be \(E_O.\)
Then, \(E_O:E_P=\)
The mid-point of side \(AB\) is \(P\) while the circumcenter of \(ABC\) is \(O\). Let the electric field at \(P\) be \(E_p\) and that at \(O\) be \(E_O.\)
Then, \(E_O:E_P=\)
| 1. | \(\dfrac{2}{9}\) | 2. | \(\dfrac{4}{9}\) |
| 3. | \(\dfrac{9}{2}\) | 4. | \(\dfrac{9}{4}\) |
Subtopic: Electric Field |
Level 3: 35%-60%
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