Concept explainers
The electric potential is given by V = 4x2z + 2xy2 − 8yz2 in a region of space, with x, y, and z in meters and V in volts.
- a. What are the x, y, and z components of the electric field in this region?
- b. What is the magnitude of the electric field at the coordinates (2.00 m, −2.00 m, 1.00 m)?
(a)
The x, y and z components of electric field in the region.
Answer to Problem 55PQ
The electric field in the regionis
Explanation of Solution
Write the equation for the electric field.
Here,
Write the equation for the the x component of the electric field.
Here,
Write the equation for the the y component of the electric field.
Here,
Write the equation for the the z component of the electric field.
Here,
Conclusion:
Substitute
Substitute
Substitute
Thus, from equation (I), write the electric field.
Thus, the electric field in the region is
(b)
The magnitude of the electric field.
Answer to Problem 55PQ
The magnitude of the electric field is
Explanation of Solution
Write the equation for the the x component of the electric field.
Write the equation for the the y component of the electric field.
Write the equation for the the z component of the electric field.
Write the equation for the magnitude of the electric field.
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Thus, the magnitude of the electric field is
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Chapter 26 Solutions
Physics for Scientist and Engineers (Foundations And Connection; Volume I and II) LLF edition
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