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Q. 70

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

In Problems 69 through 72 you are given the equation(s) used to solve a problem. For each of these,

  1. Write a realistic problem for which this is the correct equation(s).
  2. Finish the solution of the problem.

  1. If the electrostatic force acting between two identical charges separated by a distance of is , calculate the magnitude of each charge.
  2. The magnitude of each charge is calculated to be .
See the step by step solution

Step by Step Solution

Part (a) Step 1: Given Information

Equation

Part (a) Step 2: Explanation

By comparing the given equation from the equation of the electrostatic force given by two identical point charges which is given as:

We get,

Electrostatic force

Separation of point charges

Constant

Hence, it can be concluded that the electrostatic force of is generated with two identical charges at a distance of .

Part (a) Step 3: Final answer

Hence, the realistic problem that can be generated for the given question is:

If the electrostatic force acting between two identical charges separated by a distance of is , calculate the magnitude of each charge.

Part (b) Step 1: Given Information

Equation

Part (b) Step 2: Calculation

The given equation is:

Based on the equation, a realistic problem can be made as:

If the electrostatic force acting between two identical charges separated by a distance of is , calculate the magnitude of each charge.

Hence, by rearranging the terms to get the value of q,

Part (b) Step 3: Final answer 

Hence, the magnitude of each charge is calculated to be .

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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