In a hydrogen atom, electron and proton are at a distance of 0 . 5 A . The dipole moment of the system is (consider 1 A = 10 - 10 m )

Dipole moment p = q × 2 a where, q = charge, 2 a = distance between two charges For electron and proton charge q = 1 . 6 × 10 - 19 C Distance 2 a = 0 . 5 × 10 - 10 m Therefore, p = 1 . 6 × 10 - 19 × 0 . 5 × 10 - 10 p = 8 × 10 - 30 Cm

Derive an expression for potential energy of an electric dipole placed in a uniform electric field.

Consider a dipole with charges + q and - q placed in a uniform electric field as shown in the figure. The charges are separated by a distance d and the magnitude of an electric field is E . The force experienced by the charges is given as q E and - q E , as can be seen in the figure. As we know that, when a dipole is placed in a uniform electric field, both the charges as a whole do not experience any force, but it experiences a torque equal to τ which can be given as, τ = p × E = p E sin θ This torque rotates the dipole unless it is placed parallel or anti-parallel to the field. The amount of work done by the external torque can be given by d W = τ d θ W = ∫ d W = ∫ p E sin θ d θ As we know that the work done in bringing a system of charges from infinity to the given configuration is defined as the potential energy of the system, hence the potential energy can be associated with the inclination of the dipole using the above relation. The potential energy of dipole placed in an external field is zero when the angle θ is equal to 90 ° or when the dipole makes an angle of 90 ° . Considering the initial angle to be the angle at which the potential energy is zero, the potential energy of the system can be given as, U = W = ∫ 90 ° θ p E sin θ d θ U = p E - cos θ 90 ° θ U = p E ( cos 90 ° - cos θ ) U = - p E cos θ = - p · E

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Explain series and parallel combination of capacitors. Derive the formula for equivalent capacitance in each combination.

Important Questions on Electrostatic Potential and Capacitance

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Intermediate Second Year Physics>Chapter 5 - Electrostatic Potential and Capacitance>MODEL QUESTIONS (IPE PATTERN)>Q 3

Derive an expression for the energy stored in a capacitor. What is the energy stored when space between the plates is filled with a dielectric, with charging battery connected in the circuit.

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Intermediate Second Year Physics>Chapter 5 - Electrostatic Potential and Capacitance>MODEL QUESTIONS (IPE PATTERN)>Q 1

An elementary particle of mass m and charge +e initially at very large distance is projected with velocity v at a much more massive particle +Ze at rest. The closest possible distance of approach of the incident particle is

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Intermediate Second Year Physics>Chapter 5 - Electrostatic Potential and Capacitance>MODEL QUESTIONS (IPE PATTERN)>Q 2

In a hydrogen atom, electron and proton are at a distance of

Q = Q_{1} + Q_{2} + Q_{3}

. The dipole moment of the system is (consider

1 A = 10^{- 10} m

)

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Intermediate Second Year Physics>Chapter 5 - Electrostatic Potential and Capacitance>MODEL QUESTIONS (IPE PATTERN)>Q 3

There is a uniform electric field in the

X O Y

plane represented by

(40 \hat{i} + 30 \hat{j}) V m^{- 1}

. If the electric potential at the origin is

200 V

, what is the electric potential(in

V

) at the point with coordinates

(2 m, 1 m)

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Intermediate Second Year Physics>Chapter 5 - Electrostatic Potential and Capacitance>MODEL QUESTIONS (IPE PATTERN)>Q 4

An equilateral triangle has a side length $L$ . A charge $+ q$ is kept at the centroid of the triangle. $P$ is a point on the perimeter of the triangle. The ratio of the minimum and maximum possible electric potentials for the point $P$ is

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Intermediate Second Year Physics>Chapter 5 - Electrostatic Potential and Capacitance>MODEL QUESTIONS (IPE PATTERN)>Q 5

$A B C$ is an equilateral triangle of side $2 m$ . There is a uniform electric field of intensity $100 V / m$ in the plane of the triangle and parallel to $B C$ as shown. If the potential at A is $200 V$ , then the electric potentials at $B$ and $C$ are respectively.

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Intermediate Second Year Physics>Chapter 5 - Electrostatic Potential and Capacitance>MODEL QUESTIONS (IPE PATTERN)>Q 6

An electric dipole of moment

p

is placed in a uniform electric field

E

with

p

parallel to

E

. it is then rotated by an angle

q

. The work done is -

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Intermediate Second Year Physics>Chapter 5 - Electrostatic Potential and Capacitance>MODEL QUESTIONS (IPE PATTERN)>Q 7

Three identical metal plates each of area $A$ are arranged parallel to each other, $d$ is the distance between the plates as shown. A battery of $V$ volts is connected as shown. The charge stored in the system of plate is -

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Explain series and parallel combination of capacitors. Derive the formula for equivalent capacitance in each combination.

Important Questions on Electrostatic Potential and Capacitance

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