Q. No.Three identical charges (\(q\) each) are placed at the three vertices \(A,B,C\) of an equilateral triangle of side \(a.\) Let \(O\) be the centre (centroid) of the triangle \(ABC\) and \(O'\) be the reflection of \(O\) in \(BC.\) The electric field at \(O,\) due to any one of the charges, is \(E.\) The net field at \(O',\) due to all the three charges, is:
| 1. | \(2E\) | 2. | \(\Large\frac{3E}{2}\) |
| 3. | \(\Large\frac{4E}{3}\) | 4. | \(\Large\frac{5E}{4}\) |
Subtopic: Electric Field |
Level 3: 35%-60%
Hints
Given below are two statements:
| Assertion (A): | The electrostatic field of a charge distributed uniformly over the surface of a sphere vanishes within the sphere, only at its centre. |
| Reason (R): | This cancellation occurs at the centre due to the symmetry of the sphere and the symmetric, uniform charge distribution. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Electric Field |
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
Match the following charge distributions with the corresponding expressions of their electric fields: \(\left(k={\dfrac{1}{4\pi\varepsilon_0}}\right)\)
| \(\mathrm{(A)}\) | A positive point charge \(q\) is placed at the centre of an uncharged conducting sphere. Electric field is measured outside the sphere, as a function of the distance \((r)\) from the centre. |
\(\mathrm{(I)}\) | \(E=0\) |
| \(\mathrm{(B)}\) | A positive point charge \(q\) is placed within an uncharged conducting sphere, but not at its centre. Electric field is measured outside the sphere, as a function of distance \((r)\) from centre \((O).\) |
\(\mathrm{(II)}\) | \(E={\Large\frac{kq}{r^2}}\) |
| \(\mathrm{(C)}\) | A pair of point charges \((+q,-q)\) are placed within an uncharged conducting sphere, symmetrically about its centre \((O).\) 
Electric field is measured at \(P\) outside the conductor, but on the axis of the dipole. The distance \(OP=r.\) |
\(\mathrm{(III)}\) | \(E<{\Large\frac{kq}{r^2}}\) |
| \(\mathrm{(D)}\) | A positive point charge \(q\) is placed outside a spherical conductor, with the centre \(O.\)
Electric field \(E\) is measured at a point \(P,\) radially along the direction of the point charge from \(O,\) and the distance \(r\) is measured from \(q.\) |
\(\mathrm{(IV)}\) | \(E>{\Large\frac{kq}{r^2}}\) |
| 1. | \(\mathrm{A \text- I, B\text- I, C\text- III, D\text- IV}\) | 2. | \(\mathrm{A\text- II, B \text- IV, C \text- III, D \text- II}\) |
| 3. | \(\mathrm{A \text- II, B \text- II, C\text - I, D \text- III}\) | 4. | \(\mathrm{A \text- I, B \text- IV, C \text- I, D \text- IV}\) |
Subtopic: Electric Field |
52%
Level 3: 35%-60%
Hints
A thin uniform rod of mass \(M\) and length \(L\) is suspended from one of its ends, \(A\) so that it can rotate freely about it. A charge \(q\) is fixed to its lower end \(B.\) A uniform horizontal electric field is switched on, and the rod rotates about \(A,\) finally coming to equilibrium – making an angle of \(45^{\circ}\) with the vertical. If the acceleration due to gravity is \(g,\) then:
| 1. | \(qE =Mg\) | 2. | \(2qE =Mg\) |
| 3. | \(qE =2Mg\) | 4. | \(\sqrt{2}qE =Mg\) |
Subtopic: Electric Field |
Level 4: Below 35%
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%
Hints
Two infinite line charges, carrying charges \(+\lambda,-\lambda\) (per unit length) are placed parallel to each other, a short distance \(a\) apart. The electric field at a distance r from one of the charges \((A P = r)\) is:
| 1. | constant | 2. | proportional to \(\dfrac{1}{r}\) |
| 3. | proportional to \(\dfrac{1}{r^2}\) | 4. | proportional to \(\dfrac{1}{r^3}\) |
Subtopic: Electric Field |
Level 3: 35%-60%
Hints
A small conducting sphere of variable radius is given a charge \(q.\) Consider the electrostatic field at a point \(P\) outside this sphere, due to the charge.
As the radius of the sphere is slowly increased (like a balloon inflating), the electric field at \(P\):
As the radius of the sphere is slowly increased (like a balloon inflating), the electric field at \(P\):
| 1. | remains constant in magnitude and direction. |
| 2. | increases in magnitude, but retains its direction. |
| 3. | decreases in magnitude, but retains its direction. |
| 4. | changes in magnitude and direction. |
Subtopic: Electric Field |
51%
Level 3: 35%-60%
Hints
A uniformly charged sphere carrying a charge \(Q\) distributed uniformly on its outer surface is placed in an isotropic medium of dielectric constant '\(K\)'.
The electric field within the medium due to the charge \(Q\) at some point \(P\) is \(\vec E_{Q}\). The Electric field at the same point \(P\) due to induced charge within the medium is \(\vec E_{m}\). Then,
The electric field within the medium due to the charge \(Q\) at some point \(P\) is \(\vec E_{Q}\). The Electric field at the same point \(P\) due to induced charge within the medium is \(\vec E_{m}\). Then,
| 1. | \(|\vec E_m|=\left|\dfrac{\vec E_Q}{K}\right|,\) and the two fields are in opposite directions. |
| 2. | \(|\vec E_Q|=\left|\dfrac{\vec E_m}{K}\right|,\) and the two fields are in the same direction. |
| 3. | \(|\vec E_Q+\vec E_m|=\left|\dfrac{\vec E_Q}{K}\right|,\) and the two fields are in opposite directions. |
| 4. | \(|\vec E_Q+\vec E_m|=\left|\dfrac{\vec E_m}{K}\right|,\) and the two fields are in the same direction. |
Subtopic: Electric Field |
Level 3: 35%-60%
Hints
An infinitely long straight line carries a uniform positive charge \(\lambda\) per unit length. A negative point charge \((-q)\) moves in a circular path with the charge \(\lambda\) as its axis, under the action of its electric field. The kinetic energy of the point charge is:
| 1. | \({\dfrac{q\lambda}{4\pi\varepsilon_0}}\) | 2. | \({\dfrac{q\lambda}{2\pi\varepsilon_0}}\) |
| 3. | \({\dfrac{2q\lambda}{\pi\varepsilon_0}}\) | 4. | \({\dfrac{q\lambda}{8\pi\varepsilon_0}}\) |
Subtopic: Electric Field |
52%
Level 3: 35%-60%
Hints
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