# Physics questions

Jun 17th, 2015
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1. A rectangular coil measuring 20 mm by 35 mm and having 650 turns is rotating about a horizontal axis which is at right angles to a uniform magnetic field of flux density 2.5 × 10–3 T. The plane of the coil makes an angle θ with the vertical, as shown in the diagrams.

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Railgun PhysicsThe underlying physics involved in the railgun are rather simple. Current flowing through an inductor creates a magnetic field. The current flowing through the field creates a Lorentz force on the inductor tending to push the coil apart. If one portion of the coil is free to move, this portion will slide away from the power source.Qualitatively, its a relatively straightforward process. Difficulty arrises in trying to quantitatively determine the time dynamics of the electric and magnetic fields present, and an analytical description of the motion of the slug. To do so, we must examine the relationship between the current in the loop, the induced magnetic field, the motion of the slug, and the geometry of the loop - all as functions of time.We will break down the complex problem of determining the analytical equations of motion for the slug in the following way:Determine the instantaneous induced magnetic field at any point as a function of loop geometry and current in the loop at a given time.Take Faraday's Law and derive the equation for the induced EMF in the loop. Calculate this based on the magnetic field, determined above.Solve Ohm's Law for an analytical formulation of current as a function of loop resistance, initial charge in the capacitor(s), capacitance of the power cap(s), and induced EMF. Take the derivative of this equation to get an equation for I'(t) with no integrals in it.Now we need to replace I(t) and I'(t) in the above equation

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