Podcast
Questions and Answers
What happens when a dipole is placed in a uniform electric field?
What happens when a dipole is placed in a uniform electric field?
- It experiences zero net force.
- It experiences only a translational force.
- It experiences only torque. (correct)
- It experiences a net translational force in addition to torque.
What is the net force on an electric dipole in a uniform electric field?
What is the net force on an electric dipole in a uniform electric field?
- Equal to the charge.
- Equal to the electric field strength.
- Dependent on the dipole moment.
- Zero. (correct)
If an electric dipole with dipole moment $\vec{p}$ is placed in an electric field $\vec{E}$, what is the potential energy U when $\theta_1 = 90°$?
If an electric dipole with dipole moment $\vec{p}$ is placed in an electric field $\vec{E}$, what is the potential energy U when $\theta_1 = 90°$?
- $U = 0$ (correct)
- $U = pE$
- $U = -pE$
- $U = 2pE$
What represents a special differential operator when operating on electric field components?
What represents a special differential operator when operating on electric field components?
What formula represents the total work done in rotating a dipole from angle $\theta_1$ to $\theta_2$?
What formula represents the total work done in rotating a dipole from angle $\theta_1$ to $\theta_2$?
What is the expression for the torque acting on an electric dipole placed in an electric field?
What is the expression for the torque acting on an electric dipole placed in an electric field?
What does 'p' represent in the formula for torque on an electric dipole?
What does 'p' represent in the formula for torque on an electric dipole?
When is potential energy stored in the dipole?
When is potential energy stored in the dipole?
What is the effect on dipole when placed in a non-uniform electric field?
What is the effect on dipole when placed in a non-uniform electric field?
What is expression $dW$ equal to?
What is expression $dW$ equal to?
Flashcards
Dipole in Non-Uniform E Field?
Dipole in Non-Uniform E Field?
When a dipole is placed in a non-uniform electric field it experiences a net translatory force in addition to torque.
Net Force on Dipole in Uniform E?
Net Force on Dipole in Uniform E?
The net force on an electric dipole in a uniform electric field is zero.
Torque on a Dipole
Torque on a Dipole
The torque acting on an electric dipole in an electric field is given by (\tau = pE \sin \theta)
Work to Rotate Dipole
Work to Rotate Dipole
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Potential Energy (U)
Potential Energy (U)
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Total Work Done
Total Work Done
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Study Notes
- This calculates work to assemble a sphere of radius R and uniform volume charge density ρ.
- The radius of sphere is r during assembly of charge.
- Charge on sphere at that instant = (4/3)πr³ρ
- A small shell charge of thickness dr is added to the sphere of radius r.
- The charge contained in the shell = 4πr²drρ
- Work done in adding charge 4πr²drρ to the sphere containing charge (4/3)πr³ρ is given by dW = potential on surface of sphere of radius r × 4πr²drρ
- dW = (1 / 4πε₀) ((4/3)πr³ρ / r) × 4πr²drρ
- dW = (4 / 3ε₀) πρ²r⁴dr
- Total work assembling a sphere of radius R is given by W = ∫dW from r=0 to r=R
- W = ∫(4π / 3ε₀)ρ²r⁴dr from r=0 to r=R
- W = (4π / 3ε₀)ρ² ∫r⁴dr from r=0 to r=R = (4π / 3ε₀)ρ² [ r⁵ / 5 ] from 0 to R
- W = (4π / 15ε₀)ρ²R⁵
- W = (3 / 5) (1 / 4πε₀R) ((4/3)πR³ρ)²
- W = (3 / 5) (q² / 4πε₀R)
- Where q = (4/3)πR³ρ is total charge on the sphere.
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