Three identical charges ( q ) are arranged at the corners of an equilateral triangle of side a and a charge q ∘ brought to the centre of the triangle, the three charges being held fixed at its corners. How much extra work is needed to this?

Using Pythagoras theorem the length of the altitude of the triangle can be found to be 3 a 2 . Remember that the angle bisector of an equilateral triangle will bisect the opposite side. For an equilateral triangle the center O divides the altitude (since the triangle is equilateral, the length of perpendicular from any vertex will be the same.) in the ratio 2 : 1 . Let A , B and C be the three corners of the equilateral triangle. O is the centre of the triangle where charge q ∘ is brought. Therefore, the length OA will be two by third of the total length. OA = 2 3 × 3 a 2 = a 3 . Extra work done = Gain of potential energy of the system. = Kqq ∘ OA + Kqq ∘ OB + Kqq ∘ OC = 3 Kqq ∘ a 3 ∵ OA = OB = OC Therefore, work done = 3 3 Kqq ∘ a = 1 4 πε 0 3 3 qq ∘ a .

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

C = ε ο A d C = 8 p F = 8 × 10 - 12 F ε ο A d = 8 × 10 - 12 L e t t h e n e w c a p a c i tan c e b e C ' C ' = ε o k A d ' , n o w , k = 6 , d ' = d / 2 ∴ C ' = ε o × 6 × A d / 2 = 12 × ε o A d = 12 × 8 × 10 - 12 = 96 × 10 - 12 F = 96 p F .

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Draw the equipotential surface for (a) a dipole and (b) two identical negative charges placed at a certain distance apart.

Important Questions on Electrostatic Potential and Capacitance

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Gamma Question Bank for Medical Physics>Chapter 17 - Electrostatic Potential and Capacitance>Assignment>Q 29

Three identical charges

(q)

are arranged at the corners of an equilateral triangle of side a and a charge

q_{\circ}

brought to the centre of the triangle, the three charges being held fixed at its corners. How much extra work is needed to this?

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Gamma Question Bank for Medical Physics>Chapter 17 - Electrostatic Potential and Capacitance>Assignment>Q 30

Derive an expression of stored potential energy, when a dipole rotated from stable equilibrium position to any position in an external uniform electric field.

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Gamma Question Bank for Medical Physics>Chapter 17 - Electrostatic Potential and Capacitance>Assignment>Q 31

An electric dipole of dipole moment

10 μ Cm

is placed along the axis of a right angled cone such that the vertex of cone is at the centre of dipole. If the semi vertex angle of cone is

30 °

and slant height of curved surface is

20 cm

, then find the electrostatic potential at any point of circumference of base of cone

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Gamma Question Bank for Medical Physics>Chapter 17 - Electrostatic Potential and Capacitance>Assignment>Q 32

"Inside a conductor, electrostatic field is zero", why?

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Gamma Question Bank for Medical Physics>Chapter 17 - Electrostatic Potential and Capacitance>Assignment>Q 36

A slab of material of dielectric constant

k

has the same area as the plates of a parallel-plate capacitor but has a thickness

3 d / 4

, where

d

is the plate separation. How is the capacitance changed when the slab is inserted between the plates?

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Gamma Question Bank for Medical Physics>Chapter 17 - Electrostatic Potential and Capacitance>Assignment>Q 37

A network of three $10 μ F$ capacitors is connected to a $450 V$ supply, as shown in fig. Determine the charge on each capacitor.

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Gamma Question Bank for Medical Physics>Chapter 17 - Electrostatic Potential and Capacitance>Assignment>Q 39

Graphs for two capacitors of capacitances $C_{1}$ and $C_{2}$ are shown in figure. The area of plates for both capacitors are same but separation between plates is double for $C_{1}$ to that of $C_{2}$ . Which of the graph corresponds to $C_{1}$ , and $C_{2}$ and why?

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Gamma Question Bank for Medical Physics>Chapter 17 - Electrostatic Potential and Capacitance>Assignment>Q 52

(i) In the given figure, there are four point charges placed at the vertex of a square of side $7 cm$ . If $q_{1} = + 18 μ C$ , $q_{2} = - 24 μ C, q_{3} = + 35 μ C$ and $q_{4} = + 16 μ C$ , then find the electric potential at the centre $O$ of the square, assume the potential to be zero at infinity.

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(ii) An electric field $\vec{E} = (2 \hat{i} + 3 \hat{j})$ $N C^{- 1}$ exists in the space. If potential at the origin is taken to be $10$ volt, then find the potential at $(2 m, 1 m)$ .

Draw the equipotential surface for (a) a dipole and (b) two identical negative charges placed at a certain distance apart.

Important Questions on Electrostatic Potential and Capacitance

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