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Physics / Physics with MasteringPhysics 4 / Chapter 19 / Problem 33P

Physics with MasteringPhysics | 4th Edition | ISBN: 9780321541635 | Authors: James S. Walker

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IP Two point charges lie on the x axis. A charge of +9.9

Chapter 19, Problem 33P

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QUESTION:

Problem 33P

IP Two point charges lie on the x axis. A charge of +9.9 μC is at the origin, and a charge of −5.1 μC is at x = 10.0 cm. (a) At what position x would a third charge q3 be in equilibrium? (b) Does your answer to part (a) depend on whether q3 is positive or negative? Explain.

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QUESTION:

Problem 33P

IP Two point charges lie on the x axis. A charge of +9.9 μC is at the origin, and a charge of −5.1 μC is at x = 10.0 cm. (a) At what position x would a third charge q3 be in equilibrium? (b) Does your answer to part (a) depend on whether q3 is positive or negative? Explain.

ANSWER:

Step 1 of 3

(a)

Here we need to calculate the position at which the charge ${q}_{3}$ is at equilibrium between the charges ${q}_{1}=9.9\mu{}C$ and ${q}_{2}=-5.1\mu{}C$ separated by a distance $d=10\ cm$ .

Let the location of null point be $x$ from charge 1, so the distance of null point from charge 2 will be $(d-x)$ . Also at null point, the net force on charge 3 will be zero.

${F}_{3}=0$

To achieve zero net force on charge 3,we need to have forces in opposite direction with equal magnitude,

${F}_{31}={F}_{32}$

Using coulomb’s law,

$\frac{k{q}_{1}{q}_{3}}{{x}^{2}}=\frac{k{q}_{2}{q}_{3}}{(d-x{)}^{2}}$

$\frac{{q}_{1}}{{x}^{2}}=\frac{{q}_{2}}{(d-x{)}^{2}}$

$\frac{(d-x{)}^{2}}{{x}^{2}}=\frac{{q}_{3}}{{q}_{1}}$

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