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Q. 72

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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. A charge is at a distance of from the center of the dipole on the perpendicular bisector of the dipole. A line joining either charge of the dipole makes an angle of with the axis of the dipole. The total horizontal component of force on a charge q due to a dipole is . If the charge on both charges is , find the charge and show that the vertical component of force on the charge is zero.
  2. The magnitude of the charge is .
See the step by step solution

Step by Step Solution

Part (a) Step 1: Given Information

Equation:

Part (a) Step 2: Explanation

Consider the x-components of the given equation which is given as:

This equation resembles the equation of electrostatic force by a dipole which is given as:

Where,

Magnitude of the charge

Distance between the charges

Constant

Also, it can be deduced that,

Angle

Sum of horizontal forces

Hence, it can be concluded that a charge is at a distance of from the center of the dipole on the perpendicular bisector of the dipole. A line joining either charge of the dipole makes an angle of with the axis of the dipole. The total horizontal component of force on a charge q due to a dipole is . If the charge on both charges is .

Part (a) Step 3: Final answer

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

A charge is at a distance of from the center of the dipole on the perpendicular bisector of the dipole. A line joining either charge of the dipole makes an angle of with the axis of the dipole. The total horizontal component of force on a charge q due to a dipole is . If the charge on both charges is , find the charge and show that the vertical component of force on the charge is zero.

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:

A charge is at a distance of from the center of the dipole on the perpendicular bisector of the dipole. A line joining either charge of the dipole makes an angle of with the axis of the dipole. The total horizontal component of force on a charge q due to a dipole is . If the charge on both charges is , find the charge and show that the vertical component of force on the charge is zero.

Hence, by rearranging the terms of the equation of the summation of the horizontal forces to get the value of q,

Part (b) Step 3: Final answer

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

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