8 - Capacitance And Dielectrics Flashcards
What are induced dipoles?
Induced dipole refers to the dipole moment created in a nonpolar compound due to the effect of an ion nearby. Here, the ion and nonpolar compound form an interaction called the ion-induced dipole interaction. The charge of the ion induces the creation of a dipole.
If we apply an electric field to an atom or a non-polar molecule the electron could cloud will also move in response, creating an induced dipole.
What is an induced charge?
In the induction process, a charged object is brought near but not touched to a neutral conducting object. The presence of a charged object near a neutral conductor will force (or induce) electrons within the conductor to move. The movement of electrons leaves an imbalance of charge on opposite sides of the neutral conductor.
What is polarization?
Polarization is a property applying to transverse waves that specify the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave.
What is the electric dipole moment?
The electric dipole moment for a pair of opposite charges of magnitude q is defined as the magnitude of the charge times the distance between them and the defined direction is toward the positive charge.
What is polarizability?
The ratio of the induced dipole moment to the applied field is called the polarizability α of the molecule (or whatever body we have in mind). Thus
p=αE
The SI unit for α is Cm(Vm^−1)^−1 and the dimensions are M^−1T^2*Q^2
Polarizability is proportional to atomic volume, larger atoms are more polarizable
What happens to an atom when subjected to an applied field?
An electric field induces a dipole in the direction of the applied field. The dipole is proportional to field magnitude, the constant of proportionality is the polarizability of the atom. The polarizability is proportional to the volume of the atom.
What are the dipole moments of molecules?
Molecules can have dipoles. Electrons can spend more time on one atom of a covalent bond. No need to apply an electric field. Permanent dipole, not induced dipole.
Can a molecule with more than two atoms have a dipole moment?
Yes
What is the response of a molecule to an applied field?
Molecules can have dipoles. Permanent dipole, not induced dipole. In an applied field each molecule experiences a torque that tends to rotate the dipole to align with the field.
What is the work done to rotate a dipole?
Work done by a force to move an object is equal to the force in the direction of motion multiplied by the distance traveled.
W = F * d
For rotational motion, work is done by a force tangential to the rotation.
dW = F_tan (Rdθ)
Which is equal to the torque multiplied by the angle rotated.
dW = (F_tan*R)dθ
dW = τ_z dθ
Recall that the torque is a vector perpendicular to the rotation as given by the right hand rule.
What is the work done by an electric field to rotate a dipole?
dW = -pEsinθdθ
Recall the electric field acts to reduce the angle between the dipole and the field. Hence the minus sign.
What is the potential energy of a dipole in an electric field?
Work done by electric field must come from potential energy initially (conservation of energy)
U = - p * E
An electric dipole pointing in the +z-direction is placed in a uniform electric field that points in the -z-direction. What will occur initially when the electric dipole is first placed in the field?
The electric dipole will flip 180 degrees.
The electric field is uniform, so there is no net force on the dipole and it will not move in any particular direction.
There is a torque on the dipole, since the positive change of the dipole feels a force in the direction of the electric field the dipole will rotate 180 degrees so that it aligns with the field.
An electric dipole pointing in the +x-direction is at the position (d, 0, 0). There is a positive charge at the origin. Which of the following will occur initially when the electric dipole is first placed in the field?
The dipole will move towards the origin.
The negative charge of the dipole is closer to the positive charge at the origin than the positive charge of the dipole. So the Coulomb’s law attractive force between them is stronger than the repulsion between the positive charge of the dipole and the charge at the origin. Thus there is a net force on the dipole towards the origin and it will move in that direction.
The dipole is already aligned with the electric field vector in this case so it feels no torque.
Two electric dipoles pointing in the +z-direction are placed at (0,0,0) and (0,0,d). The dipoles are free to move. What will happen?
The dipoles will attract each other.
Consider the electric field of the dipole at the origin. The total field along the z-axis points in the +z direction and dies off proportional to 1/r^3.
The negative charge of the dipole at z=d is attracted to the dipole at the origin while the positive charge is repelled since it feels a force in the direction of the electric field. However, the negative charge is closer to the origin and feels a stronger force. Consequently, the net force is in the -z direction towards the dipole at the origin.
Thus the two dipoles attract each other.
