13.4 Induced electric fields  (Page 3/4)

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Summary

• A changing magnetic flux induces an electric field.
• Both the changing magnetic flux and the induced electric field are related to the induced emf from Faraday’s law.

Conceptual questions

Is the work required to accelerate a rod from rest to a speed v in a magnetic field greater than the final kinetic energy of the rod? Why?

The work is greater than the kinetic energy because it takes energy to counteract the induced emf.

The copper sheet shown below is partially in a magnetic field. When it is pulled to the right, a resisting force pulls it to the left. Explain. What happen if the sheet is pushed to the left?

Problems

Calculate the induced electric field in a 50-turn coil with a diameter of 15 cm that is placed in a spatially uniform magnetic field of magnitude 0.50 T so that the face of the coil and the magnetic field are perpendicular. This magnetic field is reduced to zero in 0.10 seconds. Assume that the magnetic field is cylindrically symmetric with respect to the central axis of the coil.

4.67 V/m

The magnetic field through a circular loop of radius 10.0 cm varies with time as shown in the accompanying figure. The field is perpendicular to the loop. Assuming cylindrical symmetry with respect to the central axis of the loop, plot the induced electric field in the loop as a function of time.

The current I through a long solenoid with n turns per meter and radius R is changing with time as given by dI / dt . Calculate the induced electric field as a function of distance r from the central axis of the solenoid.

Inside, $B={\mu }_{0}nI\text{,}\phantom{\rule{0.5em}{0ex}}\oint \stackrel{\to }{E}·d\stackrel{\to }{l}=\left(\pi {r}^{2}\right){\mu }_{0}n\frac{dI}{dt},$ so, $E=\frac{{\mu }_{0}nr}{2}·\frac{dI}{dt}$ (inside). Outside, $E\left(2\pi r\right)=\pi {R}^{2}{\mu }_{0}n\frac{dI}{dt},$ so, $E=\frac{{\mu }_{0}n{R}^{2}}{2r}·\frac{dI}{dt}$ (outside)

Calculate the electric field induced both inside and outside the solenoid of the preceding problem if $I={I}_{0}\phantom{\rule{0.2em}{0ex}}\text{sin}\phantom{\rule{0.2em}{0ex}}\omega t.$

Over a region of radius R , there is a spatially uniform magnetic field $\stackrel{\to }{B}.$ (See below.) At $t=0$ , $B=1.0\phantom{\rule{0.2em}{0ex}}\text{T,}$ after which it decreases at a constant rate to zero in 30 s. (a) What is the electric field in the regions where $r\le R$ and $r\ge R$ during that 30-s interval? (b) Assume that $R=10.0\phantom{\rule{0.2em}{0ex}}\text{cm}$ . How much work is done by the electric field on a proton that is carried once clock wise around a circular path of radius 5.0 cm? (c) How much work is done by the electric field on a proton that is carried once counterclockwise around a circular path of any radius $r\ge R$ ? (d) At the instant when $B=0.50\phantom{\rule{0.2em}{0ex}}\text{T}$ , a proton enters the magnetic field at A , moving a velocity $\stackrel{\to }{v}$ $\left(v=5.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{6}\phantom{\rule{0.2em}{0ex}}\text{m}\text{/}\text{s}\right)$ as shown. What are the electric and magnetic forces on the proton at that instant?

a. ${E}_{\text{inside}}=\frac{r}{2}\phantom{\rule{0.2em}{0ex}}\frac{dB}{dt}$ , ${E}_{\text{outside}}=\frac{{r}^{2}}{2R}\phantom{\rule{0.2em}{0ex}}\frac{dB}{dt}$ ; b. $W=4.19\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-23}\phantom{\rule{0.2em}{0ex}}\text{J}$ ; c. 0 J; d. ${F}_{\text{mag}}=4\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-13}\phantom{\rule{0.2em}{0ex}}\text{N},$ ${F}_{\text{elec}}=2.7\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-22}\phantom{\rule{0.2em}{0ex}}\text{N}$

The magnetic field at all points within the cylindrical region whose cross-section is indicated in the accompanying figure starts at 1.0 T and decreases uniformly to zero in 20 s. What is the electric field (both magnitude and direction) as a function of r , the distance from the geometric center of the region?

The current in a long solenoid of radius 3 cm is varied with time at a rate of 2 A/s. A circular loop of wire of radius 5 cm and resistance $2\phantom{\rule{0.2em}{0ex}}\text{Ω}$ surrounds the solenoid. Find the electrical current induced in the loop.

$7.1\phantom{\rule{0.2em}{0ex}}\mu \text{A}$

The current in a long solenoid of radius 3 cm and 20 turns/cm is varied with time at a rate of 2 A/s. Find the electric field at a distance of 4 cm from the center of the solenoid.

What is differential form of Gauss's law?
help me out on this question the permittivity of diamond is 1.46*10^-10.( a)what is the dielectric of diamond (b) what its susceptibility
a body is projected vertically upward of 30kmp/h how long will it take to reach a point 0.5km bellow e point of projection
i have to say. who cares. lol. why know that t all
Jeff
is this just a chat app about the openstax book?
kya ye b.sc ka hai agar haa to konsa part
what is charge quantization
it means that the total charge of a body will always be the integral multiples of basic unit charge ( e ) q = ne n : no of electrons or protons e : basic unit charge 1e = 1.602×10^-19
Riya
is the time quantized ? how ?
Mehmet
What do you meanby the statement,"Is the time quantized"
Mayowa
Can you give an explanation.
Mayowa
there are some comment on the time -quantized..
Mehmet
time is integer of the planck time, discrete..
Mehmet
planck time is travel in planck lenght of light..
Mehmet
it's says that charges does not occur in continuous form rather they are integral multiple of the elementary charge of an electron.
Tamoghna
it is just like bohr's theory. Which was angular momentum of electron is intral multiple of h/2π
determine absolute zero
The properties of a system during a reversible constant pressure non-flow process at P= 1.6bar, changes from constant volume of 0.3m³/kg at 20°C to a volume of 0.55m³/kg at 260°C. its constant pressure process is 3.205KJ/kg°C Determine: 1. Heat added, Work done, Change in Internal Energy and Change in Enthalpy
U can easily calculate work done by 2.303log(v2/v1)
Abhishek
Amount of heat added through q=ncv^delta t
Abhishek
Change in internal energy through q=Q-w
Abhishek
please how do dey get 5/9 in the conversion of Celsius and Fahrenheit
what is copper loss
this is the energy dissipated(usually in the form of heat energy) in conductors such as wires and coils due to the flow of current against the resistance of the material used in winding the coil.
Henry
it is the work done in moving a charge to a point from infinity against electric field
what is the weight of the earth in space
As w=mg where m is mass and g is gravitational force... Now if we consider the earth is in gravitational pull of sun we have to use the value of "g" of sun, so we can find the weight of eaeth in sun with reference to sun...
Prince
g is not gravitacional forcé, is acceleration of gravity of earth and is assumed constante. the "sun g" can not be constant and you should use Newton gravity forcé. by the way its not the "weight" the physical quantity that matters, is the mass
Jorge
Yeah got it... Earth and moon have specific value of g... But in case of sun ☀ it is just a huge sphere of gas...
Prince
Thats why it can't have a constant value of g ....
Prince
not true. you must know Newton gravity Law . even a cloud of gas it has mass thats al matters. and the distsnce from the center of mass of the cloud and the center of the mass of the earth
Jorge
please why is the first law of thermodynamics greater than the second
every law is important, but first law is conservation of energy, this state is the basic in physics, in this case first law is more important than other laws..
Mehmet
First Law describes o energy is changed from one form to another but not destroyed, but that second Law talk about entropy of a system increasing gradually
Mayowa
first law describes not destroyer energy to changed the form, but second law describes the fluid drection that is entropy. in this case first law is more basic accorging to me...
Mehmet
define electric image.obtain expression for electric intensity at any point on earthed conducting infinite plane due to a point charge Q placed at a distance D from it.
explain the lack of symmetry in the field of the parallel capacitor
pls. explain the lack of symmetry in the field of the parallel capacitor
Phoebe