Chapter 25: Q. 5 (page 708)

Rank in order, from most positive to most negative, the potential energies $U_{a}$ to $U_{f}$ of the six electric dipoles in the uniform electric field of FIGURE Q25.5. Explain.

Short Answer

Expert verified

Rank of the dipole from most positive to negative is $d, c, e = f, b, a$

Step by step solution

Given information and formulae used

Figure of a six-pole dipole in an electric field that is uniform.

Figure.1

Formula used:

The dipole moment's potential energy is calculated using the formula.

$U = - P E \cos θ$

Where,

$U$ is potential energy

$P$ is dipole moment

$E$ is electric field

$θ$ is the angle of dipole from the horizontal

Sort the dipoles from most positive to least positive.

(a)

Assuming that first dipole is at $0 °$

$\begin{array}{rcl} U_{a} & = & - P E \cos 0 \\ = & - P E \end{array}$

(b)

Assuming that dipole is at $θ °$

$U_{b} = - P E \cos θ$

(c)

The dipole is at $90 + θ °$

$\begin{array}{rcl} U_{c} & = & - P E \cos (90 + θ) \\ = & + P E \sin θ (here 0 ° < θ < 90 °) \end{array}$

(d)

The dipole is at $180 °$

$\begin{array}{rcl} U_{d} & = & - P E \cos 180 \\ = & + P E \end{array}$

(e)

The dipole is at $90 °$

$\begin{array}{rcl} U_{e} & = & - P E \cos 90 \\ = & 0 \end{array}$

(f)

The dipole is at $270 °$

$\begin{array}{rcl} U_{f} & = & - P E \cos 270 \\ = & 0 \end{array}$

Thus, the order of potential energy increases. $d, c, e = f, b, a$ .

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Rank in order, from most positive to most negative, the potential energies $U_{a}$ to $U_{f}$ of the six electric dipoles in the uniform electric field of FIGURE Q25.5. Explain.

Short Answer

Step by step solution

Given information and formulae used

Sort the dipoles from most positive to least positive.

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Rank in order, from most positive to most negative, the potential energiesUato Ufof the six electric dipoles in the uniform electric field of FIGURE Q25.5. Explain.

Short Answer

Step by step solution

Given information and formulae used

Sort the dipoles from most positive to least positive.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Force

Circular Motion and Gravitation

Space Physics

Oscillations

Magnetism and Electromagnetic Induction

Rotational Dynamics

Study anywhere. Anytime. Across all devices.

Rank in order, from most positive to most negative, the potential energies $U_{a}$ to $U_{f}$ of the six electric dipoles in the uniform electric field of FIGURE Q25.5. Explain.