An electric dipole is placed as shown in the figure.

The electric potential (in $10^2~\text{V}$ ) at the point $P$ due to the dipole is:
( $\varepsilon_0=$ permittivity of free space and $\dfrac{1}{4 \pi \varepsilon_0}=k$ )

1. $\left(\dfrac{8}{3}\right)qk$ 2. $\left(\dfrac{3}{8}\right)qk$

3. $\left(\dfrac{5}{8}\right)qk$ 4. $\left(\dfrac{8}{5}\right)qk$

Subtopic: Energy of Dipole in an External Field |

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Q438:

The equivalent capacitance of the arrangement shown in the figure is:

1.

30 μ F

$30~\mu \text{F}$
2.

15 μ F

$15~\mu \text{F}$
3.

25 μ F

$25~\mu\text{F}$
4.

20 μ F

$20~\mu\text{F}$

Subtopic: Combination of Capacitors |

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Q439:

If a conducting sphere of radius

R

$R$ is charged. Then the electric field at a distance

r (r > R)

$r(r>R)$ from the centre of the sphere would be, (

V =

$V=$ potential on the surface of the sphere):

1.	$\dfrac{rV}{R^2}$	2.	$\dfrac{R^2V}{r^3}$
3.	$\dfrac{RV}{r^2}$	4.	$\dfrac{V}{r}$

Subtopic: Electric Potential |

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Q436:

The equivalent capacitance of the system shown in the following circuit is:

1.	$9~{\mu \text{F}}$	2.	$2~{\mu \text{F}}$
3.	$3~{\mu \text{F}}$	4.	$6~{\mu \text{F}}$

Subtopic: Combination of Capacitors |

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Q435:

Six charges

+ q,

$+q,$

- q,

$-q,$

+ q,

$+q,$

- q,

$-q,$

+ q

$+q$ and

- q

$-q$ are fixed at the corners of a hexagon of side

d

$d$ as shown in the figure. The work done in bringing a charge

q_{0}

$q_0$ to the centre of the hexagon from infinity is:
(

ε_{0} -

$\varepsilon_0\text-$ permittivity of free space)

1.	zero	2.	$\dfrac{-q^2}{4\pi\varepsilon_0d}$
3.	$\dfrac{-q^2}{4\pi\varepsilon_0d}\Big(3-\dfrac{1}{\sqrt2}\Big)$	4.	$\dfrac{-q^2}{4\pi\varepsilon_0d}\Big(6-\dfrac{1}{\sqrt2}\Big)$

Subtopic: Electric Potential Energy |

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Q434:

The effective capacitances of two capacitors are

3 μ F

$3~\mu \text{F}$ and

16 μ F

$16~\mu \text{F}$ , when they are connected in series and parallel respectively. The capacitance of two capacitors are:
1.

10 μ F, 6 μ F

$10 ~\mu \text{F}, ~6~\mu \text{F}$
2.

8 μ F, 8 μ F

$8 ~\mu \text{F}, ~8~\mu \text{F}$
3.

12 μ F, 4 μ F

$12~\mu \text{F},~ 4~\mu \text{F}$
4.

1.2 μ F, 1.8 μ F

$1.2~\mu \text{F},~1.8~\mu \text{F}$

Subtopic: Combination of Capacitors |

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Q433:

The distance between the two plates of a parallel plate capacitor is doubled, and the area of each plate is halved. If

C

$C$ is its initial capacitance, its final capacitance is equal to:

1.	$2C$	2.	$\dfrac{C}{2}$
3.	$4C$	4.	$\dfrac{C}{4}$

Subtopic: Capacitance |

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Q432:

When a particle with charge $+q$ is thrown with an initial velocity $v$ towards another stationary change $+Q,$ it is repelled back after reaching the nearest distance $r$ from $+Q.$ The closest distance that it can reach if it is thrown with an initial velocity $2v,$ is:

1.	$\dfrac{r}{4}$	2.	$\dfrac{r}{2}$
3.	$\dfrac{r}{16}$	4.	$\dfrac{r}{8}$

Subtopic: Electric Potential Energy |

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Q431:

Three capacitors, each of capacitance

0.3 μ F

$0.3~\mu \text{F}$ are connected in parallel. This combination is connected with another capacitor of capacitance

0.1 μ F

$0.1~\mu \text{F}$ in series. Then the equivalent capacitance of the combination is:
1.

0.9 μ F

$0.9~\mu\text{F}$
2.

0.09 μ F

$0.09~\mu\text{F}$
3.

0.1 μ F

$0.1~\mu\text{F}$
4.

0.01 μ F

$0.01~\mu\text{F}$

Subtopic: Combination of Capacitors |

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Q430:

A hollow metal sphere of radius $R$ is given $+Q$ charges to its outer surface. The electric potential at a distance $\dfrac{R}{3}$ from the centre of the sphere will be:

1.	$\dfrac{1}{4\pi \varepsilon_0}\dfrac{Q}{9R}$	2.	$\dfrac{3}{4\pi \varepsilon_0}\dfrac{Q}{R}$
3.	$\dfrac{1}{4\pi \varepsilon_0}\dfrac{Q}{3R}$	4.	$\dfrac{1}{4\pi \varepsilon_0}\dfrac{Q}{R}$

Subtopic: Electric Potential |

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1.	$\left(\dfrac{8}{3}\right)qk$	2.	$\left(\dfrac{3}{8}\right)qk$
3.	$\left(\dfrac{5}{8}\right)qk$	4.	$\left(\dfrac{8}{5}\right)qk$

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