A magnetic dipole m = mk is placed in an otherwise uniform external magnetic field Be = - Bok . (a) Write an expression for the radial, polar and azimuthal components of magnetic field B(r, 0, 6) due to ñ only . (b) Show that in the combined field there exists a certain spherical surface centered on the dipole through which no field lines pass, Find its radius. (c) Sketch the magnetic field lines in the region around the dipole in presence of Bez.

A magnetic dipole moment of m = (7.50, -8.38, 4.59) Am² is inside a uniform magnetic field of B = (3.34, -6.77, 6.79) T. What is the potential energy of the dipole? (a) What is the angle between the magnetic dipole moment vector and the magnetic field vector? (b) What is the magnitude of the torque acting on the dipole?

A particle of mass “M” and charge “+Q” Travels at a velocity “V” in a plane perpendicular to a Magnetic Field of magnitude “B” as shown in the Picture. The particle will experience motion on a circular path. (not the question just context, also the pic is for probelm 1.) Assume similar conditions as problem 1 but now the proton, moves along the magnetic field undeflected. This new behavior can only be explained if there exist an external electric field in addition to the magnetic field. What is the magnitude and direction of such field? (you can disregard gravity) (prob 2 is the question:) sorry if its confusing)

b) A conductor lies in a magnetic field. The current flowing through the conductor is I = (5,9,4). The magnetic flux density is B = (–2, 4, 6). Calculate the electromagnetic force acting on the conductor by F = I x B.