For an experiment, a colleague of yours says he smeared toner particles uniformly over the surface of a sphere 1.0 m in diameter and then measured an electric field of 5000 N/C near its surface. (a) How many toner particles (Example 16–6) would have to be on the surface to produce these results? (b) What is the total mass of the toner particles? EXAMPLE 16–6 Photocopy machine. A photocopy machine works byarranging positive charges (in the pattern to be copied) on the surface of a drum,then gently sprinkling negatively charged dry toner (ink) particles onto the drum.The toner particles temporarily stick to the pattern on the drum (Fig. 16–25) andare later transferred to paper and “melted" to produce the copy. Suppose eachtoner particle has a mass of 9.0 × 10-16 kg and carries an average of 20 extraelectrons to provide an electric charge. Assuming that the electric force on atoner particle must exceed twice its weight in order to ensure sufficient attraction,compute the required electric field strength near the surface of the drum.APPROACH The electric force on a toner particle of charge q = 20e is F = qE,where E is the needed electric field. This force needs to be at least as great astwice the weight (mg) of the particle.SOLUTION The minimum value of electric field satisfies the relationqE = 2mgwhere q = 20e. Hence2(9.0 × 10-16 kg)(9.8 m/s²)20(1.6 x 10-19 C)2mgE == 5.5 × 10³ N/C.

(a) Each toner particle has 20 extra electrons. Electric field near the surface of a uniformly…

Answered: EXAMPLE 16–6 Photocopy machine. A…

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For an experiment, a colleague of yours says he smeared toner particles uniformly over the surface of a sphere 1.0 m in diameter and then measured an electric field of 5000 N/C near its surface. (a) How many toner particles (Example 16–6) would have to be on the surface to produce these results? (b) What is the total mass of the toner particles?

EXAMPLE 16–6 Photocopy machine. A photocopy machine works by
arranging positive charges (in the pattern to be copied) on the surface of a drum,
then gently sprinkling negatively charged dry toner (ink) particles onto the drum.
The toner particles temporarily stick to the pattern on the drum (Fig. 16–25) and
are later transferred to paper and “melted" to produce the copy. Suppose each
toner particle has a mass of 9.0 × 10-16 kg and carries an average of 20 extra
electrons to provide an electric charge. Assuming that the electric force on a
toner particle must exceed twice its weight in order to ensure sufficient attraction,
compute the required electric field strength near the surface of the drum.
APPROACH The electric force on a toner particle of charge q = 20e is F = qE,
where E is the needed electric field. This force needs to be at least as great as
twice the weight (mg) of the particle.
SOLUTION The minimum value of electric field satisfies the relation
qE = 2mg
where q = 20e. Hence
2(9.0 × 10-16 kg)(9.8 m/s²)
20(1.6 x 10-19 C)
2mg
E =
= 5.5 × 10³ N/C.

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