Four identical point charges ( $q$ each) are placed at the four corners of a square of diagonal $d.$ The potential at a point which is at a distance $\dfrac{d}{2}$ above the centre of the square is:
$\Big(k=\dfrac{1}{4\pi\varepsilon_0}\Big)$

1. $\dfrac{8~kq}{d}$ 2. $\dfrac{4~kq}{d}$

3. $\dfrac{4\sqrt2~kq}{d}$ 4. $\dfrac{\sqrt2~kq}{d}$

Subtopic: Electric Potential |

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Q23:

The capacitance of the system of three parallel plates of plate area

A,

$A,$ plate separation

d

$d$ is measured between the center plate

(X)

$(X)$ and the two outer plates

(Y)

$(Y)$ connected together. It is equal to:

1.

\frac{2 ε_{0} A}{d}

$\dfrac{2\varepsilon_0A}{d}$
2.

\frac{ε_{0} A}{2 d}

$\dfrac{\varepsilon_0A}{2d}$
3.

\frac{ε_{0} A}{d}

$\dfrac{\varepsilon_0A}{d}$
4.

\frac{4 ε_{0} A}{d}

$\dfrac{4\varepsilon_0A}{d}$

Subtopic: Capacitance |

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Q24:

A non-conducting circular plate is uniformly charged and the potential at its center is

V_{0} .

$V_0.$ If all the charge is collected and kept at its edge, then the potential will be:

1.	$2V_0$	2.	$\dfrac{V_0}{2}$
3.	$\dfrac{V_0}{3}$	4.	$\dfrac{V_0}{\sqrt2}$

Subtopic: Electric Potential |

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Q25:

The left plate

A

$A$ of an air capacitor is connected to the positive terminal while the right plate

B

$B$ is connected to the negative terminal of a cell of voltage

V_{0} .

$V_0.$ Assume that the plate area is

A,

$A,$ and the plate separation is

d .

$d.$ If a slab of dielectric constant

K

$K$ is inserted into the space between the plates, the electric field in the dielectric will be: (compared to the air capacitor)

1.	more.
2.	less.
3.	equal.
4.	more or less or equal depending on the value of $K$ .

Subtopic: Dielectrics in Capacitors |

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Q26:

The equivalent capacitance of the circuit between the points

A and B

$A~\text{and}~B$ is equal to:

1.

$2C$

2.

$\dfrac{3C}{2}$

3.

$3C$

4.

$\dfrac{5C}{2}$

Subtopic: Combination of Capacitors |

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Q27:

A particle

$(P)$ of mass

$m$ is placed on the axis of a uniform circular ring of radius

$R$ and mass

$M.$ Its distance

$(OP)$ from the centre

$(O)$ of the ring is equal to

$R.$ Let the net gravitational field at the centre of the ring be

$g.$ Then, the gravitational potential energy of the interaction of the system is:

1.

$-MgR$
2.

$-mgR$
3.

$\dfrac{-MgR}{\sqrt2}$
4.

$\dfrac{-mgR}{\sqrt2}$

Subtopic: Electric Potential Energy |

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Q28:

A uniformly charged metallic sphere holds a total charge

$Q_0$ and has a potential

$V_0.$ The total potential energy stored is:

1.	$Q_0V_0$	2.	$\dfrac{Q_0V_0}{2}$
3.	$\dfrac{Q_0V_0}{4}$	4.	$-Q_0V_0$

Subtopic: Electric Potential Energy |

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Q29:

Two concentric metallic spheres, surface areas

$A_1,A_2$ and separation

$d$ , have a capacitance

$C_0.$ If a parallel plate capacitor is built with the same separation

$d,$ and has the same capacitance

$C_0$ then its plate area will be:

1.	$\dfrac{A_1+A_2}{2}$	2.	$\sqrt{A_1A_2}$
3.	$\dfrac{2A_1A_2}{A_1+A_2}$	4.	$\dfrac{A_1^2A_2^2}{A_1+A_2}$

Subtopic: Capacitance |

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Q30:

Identical charges are distributed uniformly on the surfaces of a sphere and a disc of the same radius. The potential at the centre of the sphere is

$V_1,$ and the potential at the centre of the disc is

$V_2.$ The ratio

$\dfrac{V_2}{V_1}$ will be equal to:

1.	$1$	2.	$2$
3.	$4$	4.	$\sqrt2$

Subtopic: Electric Potential |

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Q31:

The circuit shown in the diagram given below, is set up with all the capacitors initially uncharged.

The potential difference between

$A$ and

$B$ when

$A$ is connected to

$X$ and

$B$ is connected to

$Y,$ is:
1.

$2.6$ V
2.

$2.4$ V
3.

$6$ V
4. zero

Subtopic: Capacitance |

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1.	$\dfrac{8~kq}{d}$	2.	$\dfrac{4~kq}{d}$
3.	$\dfrac{4\sqrt2~kq}{d}$	4.	$\dfrac{\sqrt2~kq}{d}$

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