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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

1.5×108V/m

Step by step solution

01

Given

Magnetic fieldb=0.50T

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:

uE=12ε0E2uB=12B2u0

03

Calculate the magnitude of a uniform electric field required

The electric field density is given by

uE=12ε0E2

The magnetic field density is given by

uB=12B2u0

According to the given condition,

uE=uB12ε0E2=12B2u0E2=B2μ0ε0E=Bμ0ε0E=0.50T8.85×10-12F/m4π×10-7H/mE=1.5×108V/m

Therefore, the magnitude of a uniform electric field is 1.5×108V/m.

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Most popular questions from this chapter

The switch in the circuit of Fig. 30-15 has been closed on a for a very long time when it is then thrown to b. The resulting current through the inductor is indicated in Fig. 30-28 for four sets of values for the resistance R and inductance L: (1) R=R0, (2) 2R0=R, (3) R0and2L0 , (4) 2R0and2L0. Which set goes with which curve?

In Figure, a circular loop of wire 10 cmin diameter (seen edge-on) is placed with its normal N→at an angleθ=30°with the direction of a uniform magnetic field B→of magnitude 0.50 T. The loop is then rotated such thatrotates in a cone about the field direction at the rate 100 rev/min; angleremains unchanged during the process. What is the emf induced in the loop?

A wooden toroidal core with a square cross section has an inner radius of10 cm and an outer radius of 12 cm. It is wound with one layer of wire (of diameter1.0 mmand resistance per meter 0.020Ω/m). (a) What is the inductance? (b) What is the inductive time constant of the resulting toroid? Ignore the thickness of the insulation on the wire.

Question: An electric generator contains a coil of 100 turnsof wire, each forming a rectangular loop 50.0cm to 30.0cm. The coil is placed entirely in a uniform magnetic field with magnitude B = 3.50 Tand withB⇀initially perpendicular to the coil’s plane. What is the maximum value of the emf produced when the coil is spun at 1000 rev/min about an axis perpendicular toB⇀?

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?
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