The equivalent capacitance between A and B is as the given figure:

 
1. \(16 \pi \epsilon_ 0 r\)
2. \(4 \pi \epsilon_ 0 r\)
3. \(8 \pi \epsilon_ 0 r\)
4. None of these

Subtopic:  Combination of Capacitors |
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Two metallic spheres of radii 2cm and 3cm are given charges 6mC and 4mC respectively. The final charge on the smaller sphere will be if they are connected by a conducting wire

1. 4mC

2.6mC

3. 5mC

4. 10mC

Subtopic:  Electric Potential |
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When a proton at rest is accelerated by a potential difference \(V\), its speed is found to be \(v\). The speed of an \(\alpha\text{-particle}\) when accelerated by the same potential difference from rest will be: 
1. \(v\) 2. \(v \over \sqrt{2}\)
3. \(v \sqrt{2}\) 4. \(2v\)
Subtopic:  Electric Potential |
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In the circuit shown in the figure, the energy stored in \(6~\mu\text{F}\) capacitor will be:
      

1. \(48 \times10^{-6}~\text{J}\) 2. \(32 \times10^{-6}~\text{J}\)
3. \(96 \times10^{-6}~\text{J}\) 4. \(24 \times10^{-6}~\text{J}\)
Subtopic:  Energy stored in Capacitor |
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The figure shows some of the equipotential surfaces. Magnitude and direction of the electric field is given by

 

1. 200 V/m, making an angle 1200 with the x-axis

2. 100 V/m, pointing towards the negative x-axis

3. 200 V/m, making an angle -600 with the x-axis

4. 100 V/m, making an angle 300 with the x-axis

Subtopic:  Relation between Field & Potential |
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An air capacitor of capacity C=10μF is connected to a constant voltage battery of 12 V. Now the space between the plates is filled with a liquid of dielectric constant 5. The charge that flows now from battery to the capacitor is

1. 120 μC

2. 699 μC

3. 480 μC

4. 24 μC

Subtopic:  Dielectrics in Capacitors |
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Two identical metal plates are given charges Q1 and Q2<Q1 respectively. If they are now brought close to form a parallel plate capacitor with capacitance C, the potential difference between them is :

1. Q1+Q22C

2. Q1+Q2C

3. Q1-Q2C

4. Q1-Q22C

Subtopic:  Capacitance |
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A and B are two concentric metallic shells. If A is positively charged and B is earthed, then electric

                                             

1.  Field at common centre is non-zero

2.  Field outside B is nonzero

3.  Potential outside B is positive

4.  Potential at common centre is positive

Subtopic:  Electric Potential |
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The electric potential at a point at distance 3R from the centre of disc
of radius R lying in the axis of the disc whose surface charge density is σ
will be given by:
1. σ2ε02-3R                          2. σ2ε02+3R
3.σ2ε03-2R                           4. σ2ε03+2R

Subtopic:  Electric Potential |
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A 4 μF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 2 μF capacitor. How much electrostatic energy of the first capacitor is lost in the form of heat and electromagnetic radiation?

1. 2.67×10-2 J

2. 4.99×10-2 J

3. 6.67×10-2 J

4. 8.84×10-2 J

 

Subtopic:  Energy stored in Capacitor |
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