# Three charges $$Q$$, $$+q$$ and $$+q$$ are placed at the vertices of an equilateral triangle of side $$l$$ as shown in the figure. If the net electrostatic energy of the system is zero, then $$Q$$ is equal to:             1. $$-\frac{q}{2}$$ 2. $$-q$$ 3. $$+q$$ 4. $$\text{zero}$$

Subtopic:  Electric Potential Energy |
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A thin spherical conducting shell of radius R has a charge q. Another charge Q is placed at the centre of the shell. The electrostatic potential at a point p which is at a distance $\frac{R}{2}$ from the centre of the shell is:

1. $\frac{\left(q+Q\right)}{4\pi {\epsilon }_{0}}\frac{2}{R}$

2. $\frac{2Q}{4\pi {\epsilon }_{0}R}$

3. $\frac{2Q}{4\pi {\epsilon }_{0}R}-\frac{2q}{4\pi {\epsilon }_{0}R}$

4. $\frac{2Q}{4\pi {\epsilon }_{0}R}+\frac{q}{4\pi {\epsilon }_{0}R}$

Subtopic:  Electric Potential |
62%
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A charge of 10 e.s.u. is placed at a distance of 2 cm from a charge of 40 e.s.u. and 4 cm from another charge of 20 e.s.u. The potential energy of the charge 10 e.s.u. is: (in ergs

 1 87.5 2 112.5 3 150 4 250
Subtopic:  Electric Potential Energy |
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In a certain charge distribution, all points having zero potential can be joined by a circle S. Points inside S have positive potential, and points outside S have a negative potential. A positive charge, which is free to move, is placed inside SWhat is the correct statement about S:

 1 It will remain in  equilibrium 2 It can move inside S, but it cannot cross S 3 It must cross S at some time 4 It may move, but will ultimately return to its starting point
Subtopic:  Equipotential Surfaces |
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Two charges q1 and q2 are placed 30 cm apart, as shown in the figure. A third charge q3 is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is $\frac{{q}_{3}}{4\pi {\epsilon }_{0}}k$, where k is:

 1 8q2 2 8q1 3 6q2 4 6q1
Subtopic:  Electric Potential Energy |
66%
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If the dielectric constant and dielectric strength be denoted by k and x respectively, then a material suitable for use as a dielectric in a capacitor must have:

1. high k and high x.

2. high k and low x.

3. low k and low x.

4. low k and high x.

Subtopic:  Dielectrics in Capacitors |
56%
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Three capacitors of capacitances 3 μF, 9 μF and 18 μF are connected once in series and another time in parallel. The ratio of equivalent capacitance in the two cases $\left(\frac{{C}_{s}}{{C}_{p}}\right)$ will be:

1. 1 : 15

2. 15 : 1

3. 1 : 1

4. 1 : 3

Subtopic:  Combination of Capacitors |
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Four capacitors each of capacity 3 μF are connected as shown in the adjoining figure. The ratio of equivalent capacitance between A and B and between A and C will be:

1. 4: 3

2. 3: 4

3. 2: 3

4. 3: 2

Subtopic:  Combination of Capacitors |
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A parallel plate condenser is filled with two dielectrics as shown. Area of each plate is A metre2 and the separation is t metre. The dielectric constants are k1 and k2 respectively. Its capacitance in farad will be:

1. $\frac{{\epsilon }_{0}A}{t}\left({k}_{1}+{k}_{2}\right)$

2. $\frac{{\epsilon }_{0}A}{t}.\frac{{k}_{1}+{k}_{2}}{2}$

3. $\frac{2{\epsilon }_{0}A}{t}\left({k}_{1}+{k}_{2}\right)$

4. $\frac{{\epsilon }_{0}A}{t}.\frac{{k}_{1}-{k}_{2}}{2}$

Subtopic:  Dielectrics in Capacitors |
61%
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In the connections shown in the adjoining figure, the equivalent capacity between A and B will be:

1. 10.8 μF

2. 69 μF

3. 15 μF

4. 10 μF

Subtopic:  Combination of Capacitors |
72%
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