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Chapter 23: Q. 72 (page 657)

A proton orbits a long charged wire, making 1.0脳106 revolutions per second. The radius of the orbit is 1.0cm. What is the wire鈥檚 linear charge density?

Short Answer

Expert verified

The wire鈥檚 linear charge density is-2.28nC/m

Step by step solution

01

Given information and Formula used

Given :

Proton makes revolutions per second : 1.0脳106

The radius of the orbit : 1.0cm

Theory used :

Electric field due to long charged wire at distance r

E=2位4蟺蔚0r

(Electrostatic force is attractive, therefore 位is negative.)

The proton receives centripetal force from electrostatic force, that isFc=Fe

02

Calculating the wire’s linear charge density 

Now, PE=mw2r

Using the above relation, we can deduce :

-2位脳e2蟺蔚0r=mw2r鈬�-位=1.67脳10-27脳(2蟺脳106)2脳(10-2)22脳1.6脳10-19脳9脳109=-2.28x109C/m鈬�位=-2.28nC/m

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