Electric Charges and Fields

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Electric Charges and Fields

To find the value of potential at a point, the external force at every point of the path is to be equal and opposite to the

(a) work done

(b) electrostatic force on the test charge at that point

(d) None of the above

Ans: (b) electrostatic force on the test charge at that point

The variation of electric potential of an electric dipole with distance r is

(a) $\displaystyle E\propto \frac{1}{{{{r}^{3}}}}$

(b) $\displaystyle E\propto \frac{1}{{{{r}^{2}}}}$

(d) $\displaystyle E\propto r$

Ans: (b) $\displaystyle E\propto \frac{1}{{{{r}^{2}}}}$

The potential in the equatorial plane of a dipole of a dipole moment p is

(a) infinite (b) zero

Ans: (b) zero

Two charges $\displaystyle 3\times {{10}^{{-8}}}$ C and $\displaystyle -2\times {{10}^{{-8}}}$ C located 15 cm apart. At what point on the line joining the two charges is the electric potential zero?

(a) 9 cm (b) 42 cm (c) 18 cm (d) 20 cm

Ans: (a) 9 cm

A charge 2Q is placed at each corner of a cube of side a. The potential at the centre of the cube is

(a) $\displaystyle \frac{{8Q}}{{\pi {{\in }_{0}}a}}$

(b) $\displaystyle \frac{{4Q}}{{4\pi {{\in }_{0}}a}}$

(d) $\displaystyle \frac{{2Q}}{{\pi {{\in }_{0}}a}}$

Ans: (c) $\displaystyle \frac{{8Q}}{{\sqrt{3}\pi {{\in }_{0}}a}}$

For a uniform electric field E, along the X-axis, the equipotential surfaces are plane

(a) perpendicular to Z-axis

(b) parallel to the yz-plane

(d) perpendicular to Y-axis

Ans: (b) parallel to the yz-plane

**What is the work done in moving a 2μC point charge from corner A to corner B of a square ABCD in figure, when a 10μC charge exists at the centre of the square?**

(a) Zero (b) 5

Ans: (a) Zero

Two charges of equal magnitude q are placed in air at a distance 2a apart and third charge -2q is placed at mid-point. The potential energy of the system is (∊0 = permittivity of free space)

(a) $\displaystyle -\frac{{{{q}^{2}}}}{{8\pi {{\in }_{0}}a}}$

(b) $\displaystyle -\frac{{3{{q}^{2}}}}{{8\pi {{\in }_{0}}a}}$

(d) $\displaystyle -\frac{{7{{q}^{2}}}}{{8\pi {{\in }_{0}}a}}$

Ans: (d) $\displaystyle -\frac{{7{{q}^{2}}}}{{8\pi {{\in }_{0}}a}}$

**Three point charges +q₁, – 2q and – 2q are placed at the vertices of an equilateral triangle of side a. The work done by some external force to increase their separation to 2a will be**

(a) $\displaystyle \frac{1}{{4\pi {{\in }_{0}}}}\frac{{2{{q}^{2}}}}{a}$

(b) $\displaystyle \frac{1}{{4\pi {{\in }_{0}}}}\frac{{{{q}^{2}}}}{{2a}}$

(d) zero

Ans: (d) zero

The potential difference between a cloud and the earth is 10⁷ V. Calculate the amount of energy dissipated when the charge of 100 C is transferred from the cloud to the ground due to lightning bolt.

(a) zero (b) 10⁹ J (c) 60 J (d) 10⁷ J

Ans (b) 10⁹ J

What happens when a conductor is placed in an external electric field?

(a) The electric field due to induced charge opposes the external field within the conductor

(b) In the static situation, the two fields cancel each other and the electrostatic field in the conductor is zero

(d) Neither (a) nor (b)

Ans (c) Both (a) and (b)

If a conductor is given an excess of charge, then it

(a) resides on its surface

(b) move to its centre

(d) distributes equally inside it

Ans (a) resides on its surface

The total dipole moment of dielectric with polar molecules in absence of an external electric field is

(a) zero (b) negative

Ans (a) zero

If dielectric constant and dielectric strength be denoted by K and X respectively, then a material suitable for using it as a dielectric in a capacitor must have

(a) high K and high X (b) high K and low X

Ans (a) high K and high X

The extent of polarisation depends on

(a) the dipole potential energy in the external field tending to align the dipoles with the field

(b) thermal energy tending to disrupt the alignment

(d) Neither (a) nor (b)

Ans (c) Both (a) and (b)

The maximum electric field that a dielectric medium of a capacitor can withstand without breakdown (of its insulating property) is called its

(a) polarisation (b) capacitance

Ans (c) dielectric strength

A parallel plate capacitor is connected to a 5V battery and charged. The battery is then disconnected and a glass slab is introduced between the plates, then the quantities that decrease are

(a) charge and potential difference

(b) charge and capacitance

(d) energy stored and potential difference

Ans (d) energy stored and potential difference

van de graaff generator is based on the phenomenon of corona discharge, which is used for developing

(a) electric current of order of 10× 10⁶ A

(b) electric potential of order of 10 × 10⁶ V

(d) electric charge of order of 10 × 10⁶ C

Ans (b) electric potential of order of 10 × 10⁶ V

In van de graaff generator, charge is moved from one place to other, which creates a potential difference between two points. The potential produces

(a) accelerated charged particles

(b) heating in generator

(d) None of the above

Ans (a) accelerated charged particles

Two charges 5 × 10^-8 C and –3 × 10^-8 C are located 16 cm apart. At what point from positive charge on the line joining the two charges is the electric potential zero? (Take, the potential at infinity to be zero).

(a) 6 cm (b) 8 cm (c) 10 cm (d) 30 cm

Ans (b) 8 cm

A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.

(a) 3.7 × 10^-6 V (b) 2.7 × 10⁶ V

Ans (b) 2.7 × 10⁶ V

A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF=10^-12 F). What will be the capacitance, if the distance between the plates is reduced by half and the space between them is filled with a substance of dielectric constant 6?

(a) 24 pF (b) 96 pF (c) 8 pF (d) 12 pF

Ans (b) 96 pF

Three capacitors each of capacitance 9 pF are connected in series. What is the potential difference across each capacitor, if the combination is connected to a 120 V supply?

(a) 40 V (b) 60 V (c) 80 V (d) 50 V

Ans (a) 40 V

In a parallel plate capacitor with air between the plates, each plate has an area of 6×10^-3m² and the distance between the plates is 3 mm. If this capacitor is connected to a 100 V supply, what is the charge on each plate of the capacitor?

(a) 1.77 × 10^-9 C (b) 2.77 × 10^-9 C

Ans (a) 1.77 × 10^-9 C

A 600 pF capacitor is charged by a 200 V supply, then it is disconnected from the supply and is connected to another uncharged 600 pF capacitor. How much electrostatic energy is lost in the process?

(a) 12 × 10^-6 J (b) 8 × 10^-6 J

Ans (c) 6 × 10^-6 J

**A charge of 8mC is located at the origin. Calculate the work done in taking a small charge of – 2 × 10^{– 9} C from a point P(0, 0, 3) (in cm) to a point Q (0, 4, 0) (in cm), via a point R**

(0, 6, 9) (in cm).

(a) 2.4 J (b) 1.2 J (c) 2 J (d) 3.6 J

Ans (b) 1.2 J