A one-dimensional row of positive ions, each with charge + Q and separated from its neighbors by a distance d , occupies the right-hand half of the x axis. That is, there is a + Q charge at x = 0, x = + d , x = +2 d . x = +3 d , and so on out to ∞. ( a ) If an electron is placed at the position x = − d , determine F , the magnitude of force that this row of charges exerts on the electron. ( b ) If the electron is instead placed at x = −3 d , what is the value of F ? [ Hint : The infinite sum ∑ n = 1 n = ∞ 1 n 2 = π 2 6 , where n is a positive integer.]
A one-dimensional row of positive ions, each with charge + Q and separated from its neighbors by a distance d , occupies the right-hand half of the x axis. That is, there is a + Q charge at x = 0, x = + d , x = +2 d . x = +3 d , and so on out to ∞. ( a ) If an electron is placed at the position x = − d , determine F , the magnitude of force that this row of charges exerts on the electron. ( b ) If the electron is instead placed at x = −3 d , what is the value of F ? [ Hint : The infinite sum ∑ n = 1 n = ∞ 1 n 2 = π 2 6 , where n is a positive integer.]
A one-dimensional row of positive ions, each with charge +Q and separated from its neighbors by a distance d, occupies the right-hand half of the x axis. That is, there is a +Q charge at x = 0, x = +d, x = +2d. x = +3d, and so on out to ∞. (a) If an electron is placed at the position x = −d, determine F, the magnitude of force that this row of charges exerts on the electron. (b) If the electron is instead placed at x = −3d, what is the value of F? [Hint: The infinite sum
∑
n
=
1
n
=
∞
1
n
2
=
π
2
6
, where n is a positive integer.]
A charge +q is located at the origin. A charge - 2q is at 3.15 m on the x axis.
(a) For what finite value of x is the electric field zero?
7
Xm
To the right of both charges, which charge is always closest? Does it have the smaller or larger
charge? At what locations are there two field contributions that can cancel to produce zero net
field?
(b) For what finite value(s) of x is the electric potential zero?
x m
Because the charge of -2q is closer than the charge of +q for this value of x,
the 2q dominates and the total field cannot be zero.
m
smaller value
larger value
Three charged particles lie in the x y-coordinate plane at the vertices of an equilateral triangle with side length 0.500 m. All charges are measured in µC.
Positive charge A is at the origin.
Positive charge B is in the first quadrant, along a line 60.0°counterclockwise from the positive x-axis.
Negative charge C is at (0.500, 0).
(a) Three point charges, A = 2.35 µC, B = 7.10 µC, and C =
−3.90 µC, are located at the corners of an equilateral triangle as in the figure above. Find the magnitude and direction of the electric field at the position of the 2.35 µC charge.
(a)
magnitude
N/C
direction
° below the +x-axis
(b) How would the electric field at that point be affected if the charge there were doubled?
The magnitude of the field would be halved.
The field would be unchanged.
The magnitude of the field would double.T
he magnitude of the field would quadruple.
(C) Would the magnitude of the…
One model of the atom from the early 20th century is the Thomson model, in which a spherical
positive charge, which we'll assume is uniform, contains a number of electrons. Let's further
assume that, on average, the electrons are also uniformly distributed throughout the sphere.
A) Consider one of the electrons. Excluding that electron, what is the net charge of the rest
of the atom?
B) If the atomic sphere has radius R, what is the force acting on that electron a distance r
Chapter 21 Solutions
Physics for Scientists and Engineers with Modern Physics
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