Suppose there is a square wire loop (side a), lying in the yz plane with the corners of (0,0,0), (0,a,0), (0,a,a), and (0,0,a), which carries a steady current "I". Calculate the magnetic field at (0,-a,0) point. (Hint: Use Biot-Savart Law and Superposition principle. Net field is the (vector) sum of the fields due to each side taken separately.)

A particle of mass m, charge q and position x moves in a constant, uniform magnetic field B which points in a horizontal direction. The particle is also under the influence of gravity, g , acting vertically downwards. Write down the equation of motion and show that it is invariant under translations x -> x + x0. Obtain x = \alpha x \times n + gt + a where \alpha = qB/m, n is a unit vector in the direction of B and a is a constant vector. Show that, with a suitable choice of origin, a can be written in the form a = an. By choosing suitable axes, show that the particle undergoes a helical motion with a constant horizontal drift. Suppose that you now wish to eliminate the drift by imposing a uniform electric field E. Determine the direction and magnitude of E. Training

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Calculate the magnitude of the magnetic field 1 cm from the axis of a solenoid with radius 1.5 cm, 1000 turns per meter, and current I solenoid = 1 A, and from a long wire that runs through the middle of the solenoid with current Iwire = 100 A in the -2-direction. 3 sig figs, answer in units of mT, ~1 if nonzero