Combined E&M fields – Tutorial 1

This problem is a typical JEE Main as well NEET level Physics question. However, in this post, the second question is added to ensure that the reader understands the basics very well and is comfortable with not only the Physics tricks but also the Mathematics involved. The detailed analysis of the background has been covered in the previous post. In this post we shall illustrate how and why the principle of conservation of energy should be used to save time, instead of taking the lengthier approach that has been already discussed.

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Charged Particle in Coexisting Electric and Magnetic Fields

This is a key problem for students preparing for JEE Advanced, JEE Main, and NEET (undergraduate). Many questions of varying standards and toughness can be formed on its basis, some of which have been put here in the question statement. For example, the magnetic field working perpendicular to the velocity vector all the time is not going to produce any work. Thus the question can be a little modified to be easily solved by using the Work-Energy principle so that the work done by the electric field can be equated to the kinetic energy of the particle. However, in this particular problem, that technique is useless. That’s why we must understand the Physics and Mathematics involved in this question. A short tutorial post explaining how a sample variant of this question can be asked is going to be published next.

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Bead embedded to a rotating wire

This problem can be solved in at least 3 meaningful ways, (a) from the ground frame, (b) from the rotating frame and (c) with Lagrangian. Let us do it in all of them. But even before we begin to decide whether to use Lagrangian mechanics or not, we need to understand the motion from the ground frame. It is not always advisable to use the ground frame to solve problems in rotational motion. More often than not, the ground frame calls for more variables and thus more equations than the rotational frame. However, using the rotational frame calls for fictitious or pseudo forces and without a firm understanding of the motion through the real forces, there is a big possibility of making mistakes. Hence, ThePhysicist suggests that the students, while practicing, should always try to solve problems of rotational motion from the ground frame first and then from the rotational frame.

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