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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

A problem of practical interest is to make a beam of electrons turn a 90°corner. This can be done with the parallel-plate capacitor shown in FIGURE. An electron with kinetic energy 3.0×10-17Jenters through a small hole in the bottom plate of the capacitor.

a. Should the bottom plate be charged positive or negative relative to the top plate if you want the electron to turn to the right? Explain.

b. What strength electric field is needed if the electron is to emerge from an exit hole 1.0cmaway from the entrance hole, traveling at right angles to its original direction?

Hint: The difficulty of this problem depends on how you choose your coordinate system.

c. What minimum separation dminmust the capacitor plates have?

FIGUREP23.38shows three charges at the corners of a square. Write the electric field at point Pin component form.

FIGURE is a cross section of two infinite lines of charge that extend out of the page. The linear charge densities are ±λ. Find an expression for the electric field strength Eat height yabove the midpoint between the lines.

A parallel-plate capacitor is formed from two 6.0-cm-diameter electrodes spaced 2.0mmapart. The electric field strength inside the capacitor is 1.0×106N/C. What is the charge (in nC ) on each electrode?

You’ve been assigned the task of determining the magnitude and direction of the electric field at a point in space. Give a step-by-step procedure of how you will do so. List any objects you will use, any measurements you will make, and any calculations you will need to perform. Make sure that your measurements do not disturb the charges that are creating the field.

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