AP Free Response Question
2010 C1 E&M
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A charge +Q is uniformly distributed over a quarter circle of radius R, as shown above. Points A, B, and C are located as shown, with A and C located symmetrically relative to the x-axis. Express all algebraic answers in terms of the given quantities and fundamental constants.
(a) Rank the magnitude of the electric potential at points A, B, and C from greatest to least, with number 1 being greatest. If two points have the same potential, give them the same ranking.
Justify your rankings.
Point P is at the origin, as shown below, and is the center of curvature of the charge distribution.
(b) Determine an expression for the electric potential at point P due to the charge Q.
(c) A positive point charge q with mass m is placed at point P and released from rest. Derive an expression for the speed of the point charge when it is very far from the origin.
(d) On the dot representing point P below, indicate the direction of the electric field at point P due to the charge Q.
(e) Derive an expression for the magnitude of the electric field at point P.
Topic Formulas
Description
Published Formula
Ampere's Law
Biot-Savat Law
capacitance
capacitance (dielectric)
capacitors in parallel
capacitors in series
Coulomb's Law
current density
elastic potential energy
electric current
electric field
electric field strength
electric potential energy
energy stored in a capacitor
energy stored in an inductor
Faraday's Law
force ona current-carrying wire
Gauss' Law
induced emf (inductor)
induced emf (magnetism)
Joule's Law
kinetic energy
magnetic field around a current-carrying wire
magnetic field of a solenoid
magnetic flux
magnetic force on a moving charge
motional emf
Ohm's Law
parallel-plate capacitor
potential and electric field strength
potential due to a collection of point charges
potential energy
power
power
resistance in parallel
resistance in series
resistivity
work
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