Colin DonnellyMCAT Physics and Math 5.5: Special Cases in Electrostatics
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Equipotential line
An equipotential line is a line on which the potential at every point is the same.
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The potential difference between any two points on an equipotential line is _____.
zero
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Drawn on paper, equipotential lines may look like _____. In three-dimensional space, these equipotential lines would actually be _____.
concentric circles surrounding a source charge
spheres surrounding the source charge
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_____ work is done when moving a test charge q from one point on an equipotential line to another.
Zero
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Work will be done in moving a test charge q from one equipotential line to another, but the work depends only on the _____ and not on _____.
potential difference of the two lines
the pathway taken between them
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Electric dipole
The electric dipole results from two equal and opposite charges being separated a small distance d from each other.
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The electric dipole can be _____ (as in the case of the moment-to-moment changes in electron distribution that create London dispersion forces) or _____ (as in the case of the molecular dipole of water or the carbonyl functional group).
transient
permanent
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Generic dipole diagram
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Electric potential from a dipole (close)
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Electric potential from a dipole (far, include approximations)
r2-r1 ~ dcosθ
r1r2 ~ r2
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dipole moment (with symbol)
The product of charge and separation distance is defined as the dipole moment (p): p = qd
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SI derived unit for dipole moment
C · m
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The dipole moment is a _____ quantity.
vector
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Physicists define the dipole moment vector along the line connecting the charges (the dipole axis), with the vector pointing from the _____ toward the _____.
negative charge -> positive charge
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Chemists usually have p point from the _____ toward the _____. Sometimes, chemists draw a crosshatch at the tail end of the dipole vector to indicate that the tail end is the _____.
positive charge -> negative charge
positive charge
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Common unit of dipole moment (CGS, with conversion)
1 debye (D) = 3.34 × 10−30 C · m
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Perpendicular bisector of the dipole.
The plane that lies halfway between +q and –q is called the perpendicular bisector of the dipole. Because the angle between this plane and the dipole axis is 90° (and cos 90° = 0), the electrical potential at any point along this plane is 0.
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Magnitude of the electric field on the perpendicular bisector of the dipole equation
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The electric field vectors at the points along the perpendicular bisector will point in the direction ...
... opposite to p (as defined directionally by physicists).
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In the absence of an electric field, the dipole axis can assume _____.
any random orientation
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Net torque around the center of the dipole axis derivation
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Net torque on a dipole equation
τ = pE sin θ
p is the magnitude of the dipole moment (p = qd)
E is the magnitude of the uniform external electric field
θ is the angle the dipole moment makes with the electric field
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When the electric dipole is placed in a uniform external electric field, each of the equal and opposite charges of the dipole will experience a force exerted on it by the field. Because the charges are equal and opposite, the forces acting on the charges will also be equal in magnitude and opposite in direction, resulting in a situation of _____. There will be, however, a _____ about the center of the dipole axis.
translational equilibrium (i.e. the dipole does not change velocity overall)
net torque
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For a dipole at some angle in an external electric field, there will be _____, but not _____.
translational equilibrium
rotational equilibrium
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The torque placed on a dipole will cause it to reorient itself so that ...
... its dipole moment, p, aligns with the electric field E. (physics convention, not chemistry)
