Chapter 16: Q48P (page 626)

If throughout a particular region of space the potential can be expressed as $V = 4 x z + 2 y - 5 z$ , what are the vector components of the electric field at location $(x, y, z)$ ?

Short Answer

Expert verified

The vector component of electric field at location $(x, y, z)$ is $- <4 z, 2, 4 x - 5>$ .

Step by step solution

Write the given data from the question.

The potential, $V = 4 x z + 2 y - 5 z$ .

Determine the formulas to calculate the vector components of the electric field at location x,y,z.

The expression to calculate the vector component of electrical field is given as follows.

$\vec{E} = <\frac{d}{d x}, \frac{d}{d y}, \frac{d}{d z}> (V)$ ........ (i)

Calculate the vector components of the electric field at location x,y,z.

Calculate the electrical filed.

Substitute $4 x z + 2 y - 5 z$ for $V$ into equation (i)

$\vec{E} = - <\frac{d}{d x}, \frac{d}{d y}, \frac{d}{d z}> (4 x z + 2 y - 5 z) \vec{E} = - <\frac{d}{d x} (4 x z + 2 y - 5 z), \frac{d}{d y} (4 x z + 2 y - 5 z), \frac{d}{d z} (4 x z + 2 y - 5 z)> \vec{E} = - <4 z, 2, 4 x - 5>$

Hence the vector component of electric field at location $(x, y, z)$ is $- <4 z, 2, 4 x - 5>$ .

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If throughout a particular region of space the potential can be expressed as $V = 4 x z + 2 y - 5 z$ , what are the vector components of the electric field at location $(x, y, z)$ ?

Short Answer

Step by step solution

Write the given data from the question.

Determine the formulas to calculate the vector components of the electric field at location x,y,z.

Calculate the vector components of the electric field at location x,y,z.

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If throughout a particular region of space the potential can be expressed as V=4xz+2y-5z, what are the vector components of the electric field at location (x,y,z)?

Short Answer

Step by step solution

Write the given data from the question.

Determine the formulas to calculate the vector components of the electric field at location x,y,z.

Calculate the vector components of the electric field at location x,y,z.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Magnetism

Particle Model of Matter

Famous Physicists

Modern Physics

Rotational Dynamics

Thermodynamics

Study anywhere. Anytime. Across all devices.

If throughout a particular region of space the potential can be expressed as $V = 4 x z + 2 y - 5 z$ , what are the vector components of the electric field at location $(x, y, z)$ ?