VDU_Physics_3_011

 

Solved University-Physics Problems

Physics 3:  Introduction to Electricity & Magnetism 

<<<  Induced Magnetic Field.    Ampere's Law  >>>

Javier Montenegro Joo

jmj@VirtualDynamics.Org

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<<<  Induced Magnetic Field.    Ampere's Law  >>>

(1) A long straight wire of radius R transports an electric current. Calculate the radial distance where the induced magnetic field due to this current, reduces to a half of its maximum value. (a) Out of the wire  (b) inside the wire.

Solution

The maximum induced magnetic field due to an electric current in a wire, is at the surface of the wire.  This is valid for both magnetic fields, exterior and interior.  In this problem the surface of the wire is at  r = R.

The magnetic field induced by a current in a wire is: 

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EduVirtualLab about oscillations in a rectangular membrane.-

https://www.researchgate.net/publication/318779600

 

 
(2) The propulsion system of an interstellar-travel vessel includes a long, straight, solid, cylinder of radius R.  The cylinder leads lengthwise an electrical current I whose density is  J = A r,  A = Const.  Determine: (a) the constant A  (b) the magnetic field in r ≤ R  (c) the magnetic field in r ≥ R.    

Solution.-

 

(3)  A cylindrical stream of ions (charged particles) has a transversal section of radius R and it transports an electrical current   Io   whose density    J = Ao r˛.    Determine: (a) the constant Ao (b) The current between  r = R/2   and  r = R (c)  Current between   r = 0  and   r = R/2  (d) Verify that the addition of the currents obtained in (b) and (c) equal the total current Io.

Solution.-

Note that when adding the results of parts (b) and (c) the total electric current  Io must be obtained.

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(4) A cylindrical stream of charged particles has radius R and a density of electric current that varies with the radius according to J = Ao r, where Ao is a constant and r is the radial distance measured from the axis of the stream. Determine the magnetic field induced in:  (a) r > R         (b)  r < R.

Solution.-

The magnetic field induced by the stream of charged particles in the region exterior to the stream depends on the total current in the cylinder, while the field induced in its interior region depends on a fraction of the total current.

 

(5) The sketch shows two parallel vertical cables on the plane XY. The cables are separated by a distance R and, each one transports an electrical current Io in opposite direction.  Determine the magnetic fields resulting at points A, B and C.

Solución.-

Since the XY-plane is on the plane of the sketch, the z-axis is coming out the XY-plane.

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