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Chapter 31: Q. 7 (page 901)

Show that the quantity $ε_{0} \frac{{dФ}_{e}}{d t}$ has units of current.

Short Answer

Expert verified

Unit of $ε_{0} \frac{{dФ}_{e}}{d t}$ is Ampere.

Step by step solution

01

Given Information:

We have been given an expression that we need to find the units of : $ε_{0} \frac{{dФ}_{e}}{d t}$

02

Explanation:

According to:

$ε_{0} \frac{d ϕ_{e}}{d t} = ε_{0} \frac{E A}{d t}$

$= \frac{F}{m} \frac{(\frac{V}{m}) m^{2}}{s}$ $= \frac{F V}{S}$ $= \frac{C}{V} (\frac{V}{S})$

Here F is Faraday; And its units correspond to as:

I = $\frac{C o u l o m b}{s e c}$ = Ampere (A).

Therefore the expression localid="1649877123640" $ε_{0} \frac{{dФ}_{e}}{d t}$ has units Ampere which is the same as that of current.

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Most popular questions from this chapter

A helium-neon laser emits a $1.0$ -mm-diameter laser beam with a power of $1.0 m W$ . What are the amplitudes of the electric and magnetic fields of the light wave?

A radio antenna broadcasts a $1.0 M H z$ radio wave with $25 k W$ of power. Assume that the radiation is emitted uniformly in all directions.

a. What is the wave’s intensity 30 km from the antenna?

b. What is the electric field amplitude at this distance?

What is the magnetic field amplitude of an electromagnetic wave whose electric field amplitude is $10 V / m$ $?$

Unpolarized light of intensity $I_{0}$ is incident on three polarizing filters. The axis of the first is vertical, that of the second is $45 °$ from vertical, and that of the third is horizontal. What light intensity emerges from the third filter $?$

In FIGURE P31.33, a circular loop of radius $r$ travels with speed $v$ along a charged wire having linear charge density $I$ . The wire is at rest in the laboratory frame, and it passes through the center of the loop.

a. What are $\vec{E}$ and $\vec{B}$ at a point on the loop as measured by a scientist in the laboratory? Include both strength and direction.

b. What are the fields $\vec{E}$ and $\vec{B}$ at a point on the loop as measured by a scientist in the frame of the loop?

c. Show that an experimenter in the loop’s frame sees a current $I = λ ν$ passing through the center of the loop.

d. What electric and magnetic fields would an experimenter in the loop’s frame calculate at distance r from the current of part c?

e. Show that your fields of parts b and d are the same.

See all solutions

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