1) Two spheres of the same mass m are attached to each other by a massless rod of length 2a. The spheres are charged with the same magnitude but opposite in sign. The rod is free to rotate about an axis through the center of the rod and perpendicular to the plane of motion the masses may move in (in other words, the rod can swing like a dumbbell or seesaw, with a total moment of inertia of 2ma?.) A uniform electric field E is applied to the right and the dipole aligns with the field. The dipole is then slightly rotated away from equilibrium and released. Find the period of oscillation of the system. See the diagram below: 2a E 2) A rod of length I lies on the x-axis from-/2 to 1/2. Calculate the electric field at a point P an arbitrary distance away from the y-axis. Calculate the electric field at the point P under the following conditions: a) the rod is uniformly charged b) the rod has a nonuniform charge distribution 1 = 1. (4).

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Chapter1: Units, Trigonometry. And Vectors
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1) Two spheres of the same mass m are attached to each other by a massless rod of length 2a.
The spheres are charged with the same magnitude but opposite in sign. The rod is free to rotate
about an axis through the center of the rod and perpendicular to the plane of motion the masses
may move in (in other words, the rod can swing like a dumbbell or seesaw, with a total moment
of inertia of 2ma?.)
A uniform electric field E is applied to the right and the dipole aligns with the field. The dipole is
then slightly rotated away from equilibrium and released. Find the period of oscillation of the
system. See the diagram below:
2a
E
2) A rod of length l lies on the x-axis from -l/2 to 1/2. Calculate the electric field at a point P an
arbitrary distance away from the y-axis. Calculate the electric field at the point P under the
following conditions:
a) the rod is uniformly charged
1. (4).
b) the rod has a nonuniform charge distribution 1
Transcribed Image Text:1) Two spheres of the same mass m are attached to each other by a massless rod of length 2a. The spheres are charged with the same magnitude but opposite in sign. The rod is free to rotate about an axis through the center of the rod and perpendicular to the plane of motion the masses may move in (in other words, the rod can swing like a dumbbell or seesaw, with a total moment of inertia of 2ma?.) A uniform electric field E is applied to the right and the dipole aligns with the field. The dipole is then slightly rotated away from equilibrium and released. Find the period of oscillation of the system. See the diagram below: 2a E 2) A rod of length l lies on the x-axis from -l/2 to 1/2. Calculate the electric field at a point P an arbitrary distance away from the y-axis. Calculate the electric field at the point P under the following conditions: a) the rod is uniformly charged 1. (4). b) the rod has a nonuniform charge distribution 1
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