Chapter 22: Q. 75 (page 628)

The identical small spheres shown in FIGURE CP22.75 are charged to $+ 100$ nC and $- 100$ nC. They hang as shown in a $100, 000$ N/C electric field. What is the mass of each sphere?

Short Answer

Expert verified

The mass of each sphere is $4.1 g$ .

Step by step solution

Given information

A free-body diagram for this is given below

Explanation

The net force on the given charge $- 100 nC$ is the sum of the forces coming from the positive charge, gravity, and electric field. By resolving forces in the X direction, we get

$\sum F x = F E - F e - T \cos (90 - θ) = 0 \sum F x = F E - F e - T \cos 80 = 0 \dots \dots \dots (1)$

Resolving forces in the Y direction

role="math" localid="1648482100648" $\sum F y = T \sin 80 - F G = 0 \dots \dots (2)$

Here we know that $F_{G} = m g$

Now equation(2) becomes

$T = \frac{m g}{\sin 80}$

Substitute above value in equation(1)

$F E - F e = T \cos 80 F E - F e = \sin 80 \times m g / \cos 80 F E - F e = m g / \tan 80$

We know that

$F E = q E F e = \frac{1}{4 π ε 0} \times \frac{q Q}{r^{2}}$

Solving for mass m gives

$q E - \frac{1}{4 π ε 0} \times \frac{q Q}{r^{2}} = m g / \tan 80 m = \frac{q \tan 80}{g} (E - \frac{Q}{4 π ε 0 r^{2}})$

$m = \frac{100 \times 10^{- 9} \times \tan 80}{9.8} (10^{5} - (9 \times 10^{9)} \frac{100 \times 10^{- 9}}{\sin^{2} 10}) m = 4.1 g$

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The identical small spheres shown in FIGURE CP22.75 are charged to $+ 100$ nC and $- 100$ nC. They hang as shown in a $100, 000$ N/C electric field. What is the mass of each sphere?

Short Answer

Step by step solution

Given information

Explanation

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The identical small spheres shown in FIGURE CP22.75 are charged to +100 nC and -100nC. They hang as shown in a 100,000 N/C electric field. What is the mass of each sphere?

Short Answer

Step by step solution

Given information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electrostatics

Oscillations

Torque and Rotational Motion

Magnetism and Electromagnetic Induction

Fluids

Mechanics and Materials

Study anywhere. Anytime. Across all devices.

The identical small spheres shown in FIGURE CP22.75 are charged to $+ 100$ nC and $- 100$ nC. They hang as shown in a $100, 000$ N/C electric field. What is the mass of each sphere?