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Chapter 22: Q. 75 (page 628)

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

Expert verified

The mass of each sphere is4.1g.

Step by step solution

01

Given information

A free-body diagram for this is given below

02

Explanation

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

鈭�Fx=FE-Fe-Tcos(90-胃)=0鈭�Fx=FE-Fe-Tcos80=0鈥�鈥�鈥�1

Resolving forces in the Y direction

role="math" localid="1648482100648" 鈭�Fy=Tsin80-FG=0鈥�鈥�2

Here we know that FG=mg

Now equation(2) becomes

T=mgsin80

Substitute above value in equation(1)

FE-Fe=Tcos80FE-Fe=sin80脳mg/cos80FE-Fe=mg/tan80

We know that

FE=qEFe=14蟺蔚0脳qQr2

Solving for mass m gives

qE-14蟺蔚0脳qQr2=mg/tan80m=qtan80gE-Q4蟺蔚0r2

m=100脳10-9脳tan809.8105-9脳109)100脳10-9sin210m=4.1g

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Most popular questions from this chapter

A positive point chargesQlocated atx=aand a negative point charge -Qis atx=-a.A positive chargeqcan be place anywhere on they- axis. Find an expression forFnetx, the component of the net force onq.

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