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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

$1.5 \times 10^{8} V / m$

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:

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

03

Calculate the magnitude of a uniform electric field required

The electric field density is given by

$u_{E} = \frac{1}{2} ε_{0} E^{2}$

The magnetic field density is given by

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

According to the given condition,

$u_{E} = u_{B} \frac{1}{2} ε_{0} E^{2} = \frac{1}{2} \frac{B^{2}}{u_{0}} E^{2} = \frac{B^{2}}{μ_{0} ε_{0}} E = \frac{B}{\sqrt{μ_{0} ε_{0}}} E = \frac{(0.50 T)}{\sqrt{(8.85 \times 10^{- 12} F / m) (4 π \times 10^{- 7} H / m)}} E = 1.5 \times 10^{8} V / m$

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

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Most popular questions from this chapter

Two coils connected as shown in Figure separately have inductances L₁ and L₂. Their mutual inductance is M. (a) Show that this combination can be replaced by a single coil of equivalent inductance given by

$L_{eq} = L_{1} + L_{2} + 2 M$

(b) How could the coils in Figure be reconnected to yield an equivalent inductance of

$L_{eq} = L_{1} + L_{2} - 2 M$

(This problem is an extension of Problem 47, but the requirement that the coils be far apart has been removed.)

How long would it take, following the removal of the battery, for the potential difference across the resistor in an RL circuit (with L = 2.00H, R = 3.00) to decay to 10.0% of its initial value?

A loop antenna of area $2.00 {cm}^{2}$ and resistance 5.21 mis perpendicular to a uniform magnetic field of magnitude 17.0 mT. The field magnitude drops to zero in 2.96 ms. How much thermal energy is produced in the loop by the change in field?

Figure 30-24 shows two circuits in which a conducting bar is slid at the same speed vthrough the same uniform magnetic field and along a U-shaped wire. The parallel lengths of the wire are separated by 2Lin circuit 1 and by Lin circuit 2. The current induced in circuit 1 is counter clockwise. (a) Is the magnetic field into or out of the page? (b) Is the current induced in circuit 2 clockwise or counter clockwise? (c) Is the emf induced in circuit 1 larger than, smaller than, or the same as that in circuit 2?

Figure 30-30 gives the variation with time of the potential difference $V R$ across a resistor in three circuits wired as shown in Fig. 30-16. The circuits contain the same resistance $R$ and emf $ε$ but differ in the inductance L . Rank the circuits according to the value of L, greatest first.

See all solutions

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