Physics for Scientists and Engineers
Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 30, Problem 56P

(a)

To determine

The induced electric field at a distance from central axis of solenoid.

(b)

To determine

The magnitude and direction of Poynting vector.

(c)

To determine

The flux inside the solenoid.

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Consider the situation shown in the figure. A uniform electric field in the z-direction (towards you from the paper plane) with a value given by E =a.t and a uniform magnetic field in the z-direction with a value given by B=b.t are given. Both areas are limited to a circular region with radius R. If the magnitude of the electric field induced at point a=1V/m.s, b=1T/s and P on the circumference of the circle is 9000 V/m  in 2.seconds,what is the magnitude of the magnetic field induced at point P at t =2 seconds? (in  picoTesla) (hint:in the absence of free flow, you can use time dependent maxwell equation)
A spatially uniform magnetic field is restricted in a circular region of spacewith radius of 2.5 cm and has a constant direction; see figure below. If themagnetic field varies with time t as B(t) = (25 mT/s^2)t^2, what is the magnitude of the induced electric field at a distance of 4.00 cm from the center of the magnetic field region at t = 2 s?
When the Hemholtz distance condition is satisfied the second derivative of the magnetic field with respect to z vanishes or becomes zero at the center ( point P). Show that both d2Bz/dz2 = 0 and d3Bz/dz3 = 0 at point P.
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