(III) A thin ring-shaped object of radius a contains a total charge Q uniformly distributed over its length. The electric field at a point on its axis a distance x from its center is given in Example 21–9 as E = 1 4 π ϵ 0 Q x ( x 2 + a 2 ) 3 2 . (a) Take the derivative to find where on the x axis ( x > 0) E x is a maximum. Assume Q = 6.00 μ C and a = 10.0 cm. ( b ) Calculate the electric field for x = 0 to x = +12.0 cm in steps of 0.1 cm, and make a graph of the electric field. Does the maximum of the graph coincide with the maximum of the electric field you obtained analytically? Also, calculate and graph the electric field ( c ) due to the ring, and ( d ) due to a point charge Q = 6.00 μ C at the center of the ring. Make a single graph, from x = 0 (or x = 1.0 cm) out to x = 50.0 cm in 1.0 cm steps, with two curves of the electric fields, and show that both fields converge at large distances from the center. ( e ) At what distance does the electric field of the ring differ from that of the point charge by 10%?
(III) A thin ring-shaped object of radius a contains a total charge Q uniformly distributed over its length. The electric field at a point on its axis a distance x from its center is given in Example 21–9 as E = 1 4 π ϵ 0 Q x ( x 2 + a 2 ) 3 2 . (a) Take the derivative to find where on the x axis ( x > 0) E x is a maximum. Assume Q = 6.00 μ C and a = 10.0 cm. ( b ) Calculate the electric field for x = 0 to x = +12.0 cm in steps of 0.1 cm, and make a graph of the electric field. Does the maximum of the graph coincide with the maximum of the electric field you obtained analytically? Also, calculate and graph the electric field ( c ) due to the ring, and ( d ) due to a point charge Q = 6.00 μ C at the center of the ring. Make a single graph, from x = 0 (or x = 1.0 cm) out to x = 50.0 cm in 1.0 cm steps, with two curves of the electric fields, and show that both fields converge at large distances from the center. ( e ) At what distance does the electric field of the ring differ from that of the point charge by 10%?
(III) A thin ring-shaped object of radius a contains a total charge Q uniformly distributed over its length. The electric field at a point on its axis a distance x from its center is given in Example 21–9 as
E
=
1
4
π
ϵ
0
Q
x
(
x
2
+
a
2
)
3
2
.
(a) Take the derivative to find where on the x axis (x > 0) Ex is a maximum. Assume Q = 6.00 μC and a = 10.0 cm. (b) Calculate the electric field for x = 0 to x = +12.0 cm in steps of 0.1 cm, and make a graph of the electric field. Does the maximum of the graph coincide with the maximum of the electric field you obtained analytically? Also, calculate and graph the electric field (c) due to the ring, and (d) due to a point charge Q = 6.00 μC at the center of the ring. Make a single graph, from x = 0 (or x = 1.0 cm) out to x = 50.0 cm in 1.0 cm steps, with two curves of the electric fields, and show that both fields converge at large distances from the center. (e) At what distance does the electric field of the ring differ from that of the point charge by 10%?
A simple model of a water molecule treats it as two protons (H+ ) bound to a doublycharged oxygen ion (O 2-). Picture such a water molecule with two protons located onthe y-axis at y = ±76 pm and the oxygen atom (charge -2e) located on the negative xaxis at x = -59 pm. Determine the total electric dipole moment in unit vector notation ofthe water molecule. See figure 21-43 (no figure was attached to this practice problem)
If a point charge is released from rest in a uniform electric field, will it follow a field line? Will it do so if the electric field is not uniform?
A point charge of 6 µC is located at x = -3.0 cm, and a second point charge of -10 µC is located at x = +4.0 cm. Where should a third charge of +6.0 µC be placed so that the electric field at x = 0 is zero?
Chapter 21 Solutions
Physics For Scientists & Engineers, Vols. 1 & 2, And Masteringphysics With E-book Student Access Kit (4th Edition)
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