Derive Equation 5-6 from Equation 5s
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Transient Phenomena
When a switch in a circuit is closed, the current takes some time to reach its maximum. The current in the circuit does not reach its maximum suddenly. Similarly when the switch is opened, the current takes some time to reach zero. The current does not reach zero suddenly. This phenomenon in dc circuits is known as transient phenomena.
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- A 50 g tennis ball revolves around a 2-kg bowling ball in a universe that is otherwise empty. If the orbit is circular with radius of 10 m, calculate: a) The speed of the tennis ball b) The period of its motion Take the tennis ball and the bowling ball as particles.Determine the general solution of the 1-dimensional Laplace equation on the cylinder coordinates and ball coordinates!An accretion disc may form around a black hole. This is a thin disc of orbiting matter spanning radii r = Rin to Rout around the black hole. We assume that Rout » Rin and so we make the simplifying approximation that Rout → +∞o. The disc radiates according to the following equation 3 GM D(r, 0) = 1 CM (1-[B]"). 4 3 Here, r and are the usual polar coordinates with the origin at the centre of the disc. G is the gravitational constant, M is the mass of the black hole, Rin is the disc inner radius, M is the accretion rate - all these are constants. (a) Integrate D(r, 0) over the surface of the disc to find the total radiation output of the disc. (b) Find the total radiation in the case of Rin = 6GM/c².
- I am unsure where f3 should go from the black dot and the length/direction should it be?Suppose that the universe were full of spherical objects, each of mass m and radius r, with the objects distributed uniformly throughout the universe as in the previous problem. (Assume nonrelativistic objects.) Given the density of these spherical objects (as you would have found in the previous problem), how far would you be able to see in meters, on average, before your line of sight intersected one of them? Values (note, different from the above problem): m = 3 kg r = 0.03 m Answer must be in scientific notation and include zero decimal places (1 sig fig).Suppose that A,, is a covector field, and consider the object Fμv=O₁ Av - O₂ A₁. (a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a coordinate transformation.