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

Subtopic:  Electrostatic Shielding |
 65%
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Consider the situation of the previous problem. The force on the central charge due to the shell is


1. towards left

2. towards right

3. upward

4. zero.

Previous problem: A thin, metallic spherical shell contains a charge Q on it. A point charge q is placed at the centre of the shell and another charge q1 is placed outside it as shown in figure. All the three charges are positive.
                       

Subtopic:  Electrostatic Shielding |
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A capacitor of capacitance \(C\) is charged to a potential \(V.\) The flux of the electric field through a closed surface enclosing the capacitor is:
1. \( \dfrac {CV} {\varepsilon_0}\)
2. \( \dfrac {2CV} {\varepsilon_0}\)
3. \( \dfrac {CV} {2\varepsilon_0}\)
4. zero

Subtopic:  Capacitance |
 62%
From NCERT
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Two capacitors each having capacitance \(C\) and breakdown voltage \(V\) are joined in series. The capacitance and the breakdown voltage of the combination will be:   
1. \(2C\) and \(2V\)
2. \(C/2\) and \(V/2\)
3. \(2C\) and \(V/2\)
4. \(C/2\) and \(2V\)

Subtopic:  Combination of Capacitors |
 78%
From NCERT
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Two capacitors each having capacitance \(C\) and breakdown voltage \(V\) are joined in parallel. The capacitance and the breakdown voltage of the combination will be:
1. \(2C\) and \(2V\)
2. \(C\) and \(2V\)
3. \(2C\) and \(V\)
4. \(C\) and \(V\)
Subtopic:  Combination of Capacitors |
 86%
From NCERT
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The equivalent capacitance of the combination shown in the figure is:

          
1. \(C\)
2. \(2C\)
3. \(\dfrac{C}{2}\)
4. none of these

Subtopic:  Combination of Capacitors |
 80%
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A dielectric slab is inserted between the plates of an isolated capacitor. The force between the plates will: 
1. increase
2. decrease
3. remain unchanged
4. become zero

Subtopic:  Dielectrics in Capacitors |
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The energy density in the electric field created by a point charge falls off with the distance from the point charge as

1. \(1 \over r\)

2. \(1 \over r^2\)

3. \(1 \over r^3\)

4. \(1 \over r^4\)

Subtopic:  Electric Potential |
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A parallel-plate capacitor has plates of unequal area. The larger plate is connected to the positive terminal of the battery and the smaller plate to its negative terminal. Let Q+ and Q- be the charges appearing on the positive and negative plates respectively.

1.  Q+ > Q

2.  Q+ = Q– 

3.  Q+ < Q-

4.  The information is not sufficient to decide the relation between Q+ and Q

Subtopic:  Capacitance |
 68%
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A thin metal plate P is inserted between the plates of a parallel-plate capacitor of capacitance \(C\) in such a way that its edges touch the two plates (shown in the figure). The capacitance now becomes:

      

1. \(C/2\)
2. \(2C\)
3. \(0\)
4. \(\infty \)

Subtopic:  Capacitance |
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