Learning Materials
Features
Discover
Chapter 7: Q10P (page 311)
A square loop (side a) is mounted on a vertical shaft and rotated at angular velocity (Fig. 7.19). A uniform magnetic field B points to the right. Find thefor this alternating current generator.
The induced emf in the square loop is .
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
Suppose a magnetic monopole passes through a resistanceless loop of wire with self-inductance L . What current is induced in the loop?
A square loop of wire (side a) lies on a table, a distance s from a very long straight wire, which carries a current I, as shown in Fig. 7.18.
(a) Find the flux of B through the loop.
(b) If someone now pulls the loop directly away from the wire, at speed, V what emf is generated? In what direction (clockwise or counter clockwise) does the current flow?
(c) What if the loop is pulled to the right at speed V ?
An infinite wire runs along the z axis; it carries a current I (z) that is a function ofz(but not of t ), and a charge density that is a function of t (but not of z ).
(a) By examining the charge flowing into a segment dz in a time dt, show that . If we stipulate that and , show that , , where k is a constant.
(b) Assume for a moment that the process is quasistatic, so the fields are given by Eqs. 2.9 and 5.38. Show that these are in fact the exact fields, by confirming that all four of Maxwell's equations are satisfied. (First do it in differential form, for the region s > 0, then in integral form for the appropriate Gaussian cylinder/Amperian loop straddling the axis.)
A familiar demonstration of superconductivity (Prob. 7.44) is the levitation of a magnet over a piece of superconducting material. This phenomenon can be analyzed using the method of images. Treat the magnet as a perfect dipole , m a height z above the origin (and constrained to point in the z direction), and pretend that the superconductor occupies the entire half-space below the xy plane. Because of the Meissner effect, B = 0 for , and since B is divergenceless, the normal ( z) component is continuous, so just above the surface. This boundary condition is met by the image configuration in which an identical dipole is placed at - z , as a stand-in for the superconductor; the two arrangements therefore produce the same magnetic field in the region z>0.
(a) Which way should the image dipole point (+ z or -z)?
(b) Find the force on the magnet due to the induced currents in the superconductor (which is to say, the force due to the image dipole). Set it equal to Mg (where M is the mass of the magnet) to determine the height h at which the magnet will "float." [Hint: Refer to Prob. 6.3.]
(c) The induced current on the surface of the superconductor ( xy the plane) can be determined from the boundary condition on the tangential component of B (Eq. 5.76): . Using the field you get from the image configuration, show that
where r is the distance from the origin.
Question:Calculate the energy stored in the toroidal coil of Ex. 7.11, by applying Eq. 7.35. Use the answer to check Eq. 7.28.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Exams 
GCSE 
IGCSE 
AS 
A Level 
International A Level 
University Admissions Tests 
Flashcards 
Vaia AI 
Notes 
Study Plans 
Study Sets 
Find a job 
Find a degree 
Student Deals 
Magazine 
Mobile App