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See how an electric dipole with a specific strength reacts to a certain electric field. Calculate the energy needed to change it from a position where it’s balanced to one where it’s not.
An Electric Dipole having a dipole moment of 4 × 10^-9 cm is placed in a uniform electric field such that the dipole is in stable equilibrium. If the magnitude of the electric field is 3 × 10^3 n/c, What is the work done in rotating the dipole to a position of unstable equilibrium?
To find the work done in rotating the dipole to a position of unstable equilibrium, let’s first understand the concept of stable and unstable equilibrium for an electric dipole.
A stable equilibrium is when the electric dipole moment is aligned with the electric field, while an unstable equilibrium is when the dipole moment is anti-aligned with the electric field.
Given:
- Dipole moment, p = 4 × 10^-9 Cm
- Magnitude of the electric field, E = 3 × 10^3 N/C
The work done in rotating the dipole from stable to unstable equilibrium can be calculated using the formula:
The change in potential energy, ΔU = U_unstable – U_stable = 2pE
Substitute the given values:
ΔU = 2(4 × 10^-9 Cm) × (3 × 10^3 N/C)
ΔU = 2 × 12 × 10^-6 J
ΔU = 24 × 10^-6 J
ΔU = 2.4 × 10^-5 J
So, the work done in rotating the dipole to a position of unstable equilibrium is 2.4 × 10^-5 J.
What is Electrostatics?
Electrostatics is a branch of physics that deals with the study of stationary electric charges and their interactions. It primarily focuses on the behavior of electric charges at rest, as opposed to dynamic electric currents found in electromagnetism.
Key concepts in electrostatics include:
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Electric charge: Electric charge is a fundamental property of matter, and it can be positive or negative. Like charges repel each other, while opposite charges attract each other.
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Coulomb’s law: Coulomb’s law describes the electrostatic force between two charged objects. It states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
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Electric field: An electric field is a region around a charged object where the influence of its charge is felt on other charged objects. Electric field lines indicate the direction of the force that a positive test charge would experience if placed in the field.
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Electric potential: Electric potential (voltage) is the amount of work needed to move a unit positive charge from a reference point to a specific point in the electric field. It’s measured in volts (V).
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Electric potential energy: Electric potential energy is the energy possessed by a charged object due to its position in an electric field. It’s directly related to the amount of work required to bring charges together or move them apart.
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Gauss’s law: Gauss’s law relates the electric flux through a closed surface to the total charge enclosed by that surface. It is a fundamental principle used to calculate electric fields in various situations.
Applications of electrostatics include the operation of devices like capacitors, Van de Graaff generators, and electrostatic precipitators. It also plays a crucial role in understanding phenomena such as lightning, static electricity, and the behavior of charged particles in plasmas.
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