A student makes a short electromagnet by winding 390 turns of wire around a wooden cylinder of diameter d = 4.1 cm. The coil is connected to a battery producing a current of 4.1 A in the wire. (a) What is the magnitude of the magnetic dipole moment of this device? (b) At what axial distance z>>d will the magnetic field have the magnitude 4.8 µT (approximately one-tenth that of Earth's magnetic field)?

A particle having mass m  = 2.80E-4 kg carries a negative charge q= −1.70E-6 C . The particle is given an initial velocity in the −y direction (downward), as shown in the figure, of v = 7.84E2 m/s. Everywhere in space there is a uniform constant magnetic field B = 0.340 T pointing in the +z  direction, which is out of the plane of the page. What is the speed of the particle after 7 periods of the cyclotron motion (in m/s)?

Problem 10: A magnetic needle with magnetic moment μ-0.065 Am2 is placed in a uniform magnetic field B0.65 T as shown in the figure. The angle between the direction of the magnetic moment and the direction of the magnetic field is θ 250 Randomized Variables μ= 0.065 Arn B- 0.65T θ 250 Δ Part (a) Express the potential energy U in terms oft, B, θ. | cos(p) sin(p) | cos(α) sin(a) cos(0) sin(0) ( HOMI 4 5 6 BACKSPACE CLEAR Submit Hint I give up! Hints: 1% deduction per hint. Hints remaining: 1 Feedback: 1% deduction per feedback. Part (b) Calculate the numerical value of U in J. Part (c) If θ can be changed, which value has the minimum potential energy? Part (d) If θ can be changed, which value has the maximum potential energy in degrees? Δ Part (e) Ignore the mass of the needle, express the work needed to change the angle from θ to α in terms oftı, B, θ, α Part (f) If α-1500, calculate the numerical value of the work in J.

A rod of mass 0.720 kg and radius 6.00 cm rests on two parallel rails (see figure below) that are d = 12.0 cm apart and L = 45.0 cm long. The rod carries a current of I = 36.0 A in the direction shown and rolls along the rails without slipping. A uniform magnetic field of magnitude 0.400 T is directed perpendicular to the rod and the rails. If it starts from rest, what is the speed of the rod as it leaves the rails? (Assume that the rod is of uniform density.) L 2.07 X You appear to have omitted the translational kinetic energy of the rod. m/s