(III) Two positive charges + Q are affixed rigidly to the x axis, one at x = + d and the other at x = − d . A third charge + q of mass m , which is constrained to move only along the x axis, is displaced from the origin by a small distance s << d and then released from rest. ( a ) Show that (to a good approximation) + q will execute simple harmonic motion and determine an expression for its oscillation period T . ( b ) If these three charges are each singly ionized sodium atoms ( q = Q = + e ) at the equilibrium spacing d = 3 × 10 −10 m typical of the atomic spacing in a solid, find Τ in picoseconds.
(III) Two positive charges + Q are affixed rigidly to the x axis, one at x = + d and the other at x = − d . A third charge + q of mass m , which is constrained to move only along the x axis, is displaced from the origin by a small distance s << d and then released from rest. ( a ) Show that (to a good approximation) + q will execute simple harmonic motion and determine an expression for its oscillation period T . ( b ) If these three charges are each singly ionized sodium atoms ( q = Q = + e ) at the equilibrium spacing d = 3 × 10 −10 m typical of the atomic spacing in a solid, find Τ in picoseconds.
(III) Two positive charges +Q are affixed rigidly to the x axis, one at x = +d and the other at x = −d. A third charge +q of mass m, which is constrained to move only along the x axis, is displaced from the origin by a small distance s << d and then released from rest. (a) Show that (to a good approximation) +q will execute simple harmonic motion and determine an expression for its oscillation period T. (b) If these three charges are each singly ionized sodium atoms (q = Q = +e) at the equilibrium spacing d = 3 × 10−10 m typical of the atomic spacing in a solid, find Τ in picoseconds.
Definition Definition Special type of oscillation where the force of restoration is directly proportional to the displacement of the object from its mean or initial position. If an object is in motion such that the acceleration of the object is directly proportional to its displacement (which helps the moving object return to its resting position) then the object is said to undergo a simple harmonic motion. An object undergoing SHM always moves like a wave.
Two identical particles, each having charge +q, are fixed in space and separated by a distance d. A third particle with charge −Q is free to move and lies initially at rest on the perpendicular bisector of the two fixed charges a distance x from the midpoint between those charges (Fig.). (a) Show that if x is small compared with d, the motion of −Q is simple harmonic along the perpendicular bisector. (b) Determine the period of that motion. (c) Howfast will the charge −Q be moving when it is at the midpoint between the two fixed charges if initially it is released at a distance a << d from the midpoint?
Two identical particles, each having charge +q, are fixed in space and separated by a distance d. A third particle with charge -Q is free to move and lies initially at rest on the perpendicular bisector of the two fixed charges a distance x from the midpoint between those charges (as shown). (a) Show that if x is small compared with d, the motion of -Q is simple harmonic along the perpendicular bisector. (b) Determine the period of that motion. (c) How fast will the charge -Q be moving when it is at the midpoint between the two fixed charges if initially it is released at a distance a << d from the midpoint?
Two identical point charges, each with charge
+q, are fixed in space and separated by a
distance "d". A third point charge -Q of mass
"m"
It can move freely and is initially at rest on the
x-axis at a distance "x"
+q
d/2
0
d/2
+q
-Q
X
Prove that for very small "x" (x<
Chapter 21 Solutions
Physics for Scientists and Engineers with Modern Physics
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.