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

Short Answer

Expert verified

The wire’s linear charge density is-2.28nC/m

Step by step solution

01

Given information and Formula used

Given :

Proton makes revolutions per second : 1.0×106

The radius of the orbit : 1.0cm

Theory used :

Electric field due to long charged wire at distance r

E=2λ4πε0r

(Electrostatic force is attractive, therefore λis 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 :

-2λ×e2πε0r=mw2r-λ=1.67×10-27×(2π×106)2×(10-2)22×1.6×10-19×9×109=-2.28x109C/mλ=-2.28nC/m

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