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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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Most popular questions from this chapter

Your physics assignment is to figure out a way to use electricity to launch a small 6.0-cm-long plastic drink stirrer. You decide that you’ll charge the little plastic rod by rubbing it with fur, then hold it near a long, charged wire, as shown in FIGURE P23.56. When you let go, the electric force of the wire on the plastic rod will shoot it away. Suppose you can uniformly charge the plastic stirrer to 10nCand that the linear charge density of the long wire is 1.0×10-7C/m. What is the net electric force on the plastic stirrer if the end closest to the wire is 2.0cmaway?

Hint: The stirrer cannot be modeled as a point charge; an integration is required.

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A parallel-plate capacitor consists of two square plates, size L×L, separated by distance d. The plates are given charge±Q. What is the ratio Ef/Eiof the final to initial electric field strengths if

(a) Q is doubled,

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