Concept explainers
(a)
The proof for
(a)
Answer to Problem 71CP
The electric potential at the point
Explanation of Solution
The following figure shows the diagram of the dipoles and the point
Figure-(1)
The dipole moment’s magnitude is given as.
Here,
Write the equation for the electric potential at the point
Here,
Write the equation for the distance between the positive charge and the point
Write the equation for the distance between the negative charge and the point
Rearrange the equation (II) and (III) to calculate
Expand the above equation binomially and neglect the higher terms to calculate
Substitute
Substitute
Therefore, the electric potential at the point
(b)
The electric field’s radial component
(b)
Answer to Problem 71CP
The electric field’s radial component is
Explanation of Solution
Write the equation for the radial component of the electric field.
Here,
Write the equation for the perpendicular component of the electric field.
Here,
Conclusion:
Substitute
Substitute
Therefore, the electric field’s radial component is
(c)
Whether the results for
(c)
Answer to Problem 71CP
Yes, the results for
Explanation of Solution
Write the equation for
Write the equation for
Conclusion:
Substitute
Substitute
Substitute
Substitute
Therefore, the results for
(d)
Whether the results for
(d)
Answer to Problem 71CP
No, the results for
Explanation of Solution
Write the equation for
Write the equation for
Conclusion:
Substitute
Substitute
Therefore, the results for
(e)
The expression for the electric potential in terms of the Cartesian coordinates.
(e)
Answer to Problem 71CP
The expression for the electric potential in terms of the Cartesian coordinates is
Explanation of Solution
Write the equation for the electric potential.
Conclusion:
Substitute
Therefore, the expression for the electric potential in terms of the Cartesian coordinates is
(f)
The
(f)
Answer to Problem 71CP
The
Explanation of Solution
Write the equation for the
Here,
Write the equation for the
Here,
Conclusion:
Substitute
Substitute
Therefore, the
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Chapter 25 Solutions
Physics for Scientists and Engineers with Modern Physics, Technology Update
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