AP Free Response Question
2000 C2 E&M
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Three particles, A, B, and C, have equal positive charges Q and are held in place at the vertices of an equilateral triangle with sides of length
, as shown in the figure below. The dotted lines represent the bisectors for each side. The base of the triangle lies on the x-axis, and the altitude of the triangle lies on the y-axis.
i. Point P
_{1}
, the intersection of the three bisectors, locates the geometric center of the triangle and is one point where the electric field is zero. On Figure 1, draw the electric field vectors E
_{A}
, E
_{B}
, and E
_{C}
at P
_{1}
due to each of these charges. Be sure your arrows are drawn to reflect the relative magnitude of the fields.
ii. Another point where the electric field is zero is point P
_{2}
at (0,y
_{2}
). On Figure 2, draw electric field vectors E
_{A}
, E
_{B}
, and E
_{C}
at P
_{2}
due to each of the three point charges. Also indicate in the chart below whether the magnitude of each of these vectors is greater than, less than, or the same as for point P
_{1}
.
(b) Explain why the x-component of the total electric field is zero at any point on the y-axis.
(c) Write a general expression for the electric potential V at any point on the y-axis inside the triangle in terms of Q,
, and y.
(d) Describe how the answer to part (c) could be used to determine the y-coordinates of points P
_{1}
and P
_{2}
at which the electric field is zero. (You do not need to actually determine these coordinates.)
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
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
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
resistance in parallel
resistance in series
resistivity
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