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Q. 36

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

Two spheres are charged equally and placed apart. When released, they begin to accelerate at . What is the magnitude of the charge on each sphere?

is the magnitude of charge in the sphere.

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Step by Step Solution

Step 1: Introduction

A mathematical object's volume, or size, is a quality that indicates whether it is larger or smaller than other objects of the same kind. The stated result of an arrangement —of the class of objects to something that relates —is an object's magnitude.

Step 2: Find the magnitude of charge

Along the line that joins their centres, the two spheres simultaneously acted upon by a stress of equal size and opposing direction. Coulomb's law determines the magnitude of this foce.

with denotes each structure's charge and denotes the distance between their centres. Newton's second law states that the total between acceleration and force.

We have

Substitute in

Already we have

And . Incorporating this into the charge expression

.

Most popular questions for Physics Textbooks

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 or 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.

  1. The average distance between ionizing collisions is . (The electron’s mean free path is less than this, but most collisions are elastic collisions in which the electron bounces with no loss of energy.) What acceleration must an electron have to gain of kinetic energy in this distance?
  2. What force must act on an electron to give it the acceleration found in part a?
  3. What strength electric field will exert this much force on an electron? This is the breakdown field strength. Note: The measured breakdown field strength is a little less than your calculated value because our model of the process is a bit too simple. Even so, your calculated value is close.
  4. Suppose a free electron in air is 1.0 cm away from a point charge. What minimum charge is needed to cause a breakdown and create a spark as the electron moves toward the point charge?

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