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Chapter 30: Q69P (page 900)

What must be the magnitude of a uniform electric field if it is to have the same energy density as that possessed by a 0.50 T magnetic field?

Short Answer

Expert verified

$1.5 脳 10^{8} V / m$

Step by step solution

01

Given

Magnetic field $b = 0.50 T$

02

Understanding the concept

We use the formula of energy density in the magnetic field and energy density in an electric field to find the magnitude of a uniform electric field if it is to have the same energy density as that possessed by amagnetic field.

Formula:

$u_{E} = \frac{1}{2} 蔚_{0} E^{2} u_{B} = \frac{1}{2} \frac{B^{2}}{u_{0}}$

03

Calculate the magnitude of a uniform electric field required

The electric field density is given by

$u_{E} = \frac{1}{2} 蔚_{0} E^{2}$

The magnetic field density is given by

$u_{B} = \frac{1}{2} \frac{B^{2}}{u_{0}}$

According to the given condition,

$u_{E} = u_{B} \frac{1}{2} 蔚_{0} E^{2} = \frac{1}{2} \frac{B^{2}}{u_{0}} E^{2} = \frac{B^{2}}{渭_{0} 蔚_{0}} E = \frac{B}{\sqrt{渭_{0} 蔚_{0}}} E = \frac{(0.50 T)}{\sqrt{(8.85 脳 10^{- 12} F / m) (4 蟺脳 10^{- 7} H / m)}} E = 1.5 脳 10^{8} V / m$

Therefore, the magnitude of a uniform electric field is $1.5 脳 10^{8} V / m$ .

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Most popular questions from this chapter

A certain elastic conducting material is stretched into a circular loop of 12.0 cm radius. It is placed with its plane perpendicular to a uniform 0.800 Tmagnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of 75.0cm/s. What emf is induced in the loop at that instant?

The current i through a 4.6 Hinductor varies with time t as shown by the graph of Figure, where the vertical axis scale is set by $i_{s} = 8.0 A$ and the horizontal axis scale is set by $t_{s} = 6.0 m s$ . The inductor has a resistance of $12 惟$ .(a) Find the magnitude of the induced emf $蔚$ during time intervals 0 to 2 ms. (b) Find the magnitude of the induced emf $蔚$ during time intervals 2 ms to 5 ms. (c) Find the magnitude of the induced emf $蔚$ during time intervals 5 ms to 6 ms. (Ignore the behavior at the ends of the intervals.)

At time $t = 0, a 蔚 = 45 V$ potential difference is suddenly applied to the leads of a coil with inductance $L =50 mH$ and resistance $R = 180$ . At what rate is the current through the coil increasing at $t = 1.2 m s$ ?

In Fig. 30-77, $R_{1} = 8.0 惟, R_{2} = 10 惟, L_{1} = 0.30 H, L_{2} = 0.20 H$ and the ideal battery has $蔚 = 6.0 V$ . (a) Just after switch S is closed, at what rate is the current in inductor 1 changing? (b) When the circuit is in the steady state, what is the current in inductor 1?

In Figure, a wire loop of lengths L = 40.0 cmand W = 25.0 cmlies in a magnetic field $\overset{鈫�}{B}$ .(a)What is the magnitude $蔚$ if $\overset{鈫�}{B} = (4.00 脳 10^{- 2} \frac{T}{m}) y \hat{k}$ ?(b)What is the direction (clockwise or counterclockwise鈥攐r 鈥渘one鈥� if 0) of the emf induced in the loop if $\overset{鈫�}{B} = (4.00 脳 10^{- 2} \frac{T}{m}) y \hat{k}$ ?(c)What is the $蔚$ if $\overset{鈫�}{B} = (6.00 脳 10^{- 2} \frac{T}{s}) t \hat{k}$ (d)what is the direction if $\overset{鈫�}{B} = (6.00 脳 10^{- 2} \frac{T}{s}) t \hat{k}$ (e)What is the $蔚$ if $\overset{鈫�}{B} = (8.00 脳 10^{- 2} \frac{T}{m . s}) y t \hat{k}$ (f)What is the direction if $\overset{鈫�}{B} = (6.00 脳 10^{- 2} \frac{T}{s}) t \hat{k}$ (g)What is the $蔚$ if $\overset{鈫�}{B} = (3.00 脳 10^{- 2} \frac{T}{m . s}) x t \hat{k}$ (h)What is the direction if $\overset{鈫�}{B} = (3.00 脳 10^{- 2} \frac{T}{m . s}) x t \hat{k}$ (i)What is the if $\overset{鈫�}{B} = (5.00 脳 10^{- 2} \frac{T}{m . s}) y t \hat{k}$ (j)What is the direction if $\overset{鈫�}{B} = (5.00 脳 10^{- 2} \frac{T}{m . s}) y t \hat{k}$

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