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Chapter 22: Q. 40 (page 625)

ObjectsAandBare both positively charged. Both have a mass of100g, butAhas twice the charge of B. WhenAand Bare placed10cmapart,B experiences an electric force of0.45N.

a. What is the charge onA?

b. If the objects are released, what is the initial acceleration ofA?

Short Answer

Expert verified

a. Charge onAis1×10-6C.

b. The initial acceleration is4.5ms2.

Step by step solution

01

Calculation for charge (part a)

a.

The equation F=kq1q2r2used.

Where,

k=9×109Nm2C2

Charge is,

q1F=kq112q1r2

→Fr2=kq112q1

→2Fr2=kq12→2Fr2k

=q1

Where FAB=FBA=0.45Nand r=10cm=10×10-2m

So,

q1=2(0.45N)10×10-2m29×109Nm2C2

q1=1×10-6C

02

Calculation for initial acceleration (part b)

b.

Force is,

F=m×a

Acceleration is,

a=Fm

So,

role="math" a=0.45N0.1Kg

a=4.5ms2

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You sometimes create a spark when you touch a doorknob after shuffling your feet on a carpet. Why? The air always has a few free electrons that have been kicked out of atoms by cosmic rays. If an electric field is present, a free electron is accelerated until it collides with an air molecule. Most such collisions are elastic, so the electron collides, accelerates, collides, accelerates, and so on, gradually gaining speed. But if the electron’s kinetic energy just before a collision is 2.0×10-18Jor more, it has sufficient energy to kick an electron out of the molecule it hits. Where there was one free electron, now there are two! Each of these can then accelerate, hit a molecule, and kick out another electron. Then there will be four free electrons. In other words, as FIGURE P22.61 shows, a sufficiently strong electric field causes a “chain reaction” of electron production. This is called a breakdown of the air. The current of moving electrons is what gives you the shock, and a spark is generated when the electrons recombine with the positive ions and give off excess energy as a burst of light.

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