Problem 23A macmillan learning nsider a long solenoid consisting of a coil of wi

Question

Problem 23A

macmillan learning nsider a long solenoid consisting of a coil of wire with radius R and n turns per unit length. The solenoid arries a current I as shown in the figures. Using symmetry and Ampere's Law, you will find the magnitude and direction of the magnetic field inside the solenoid. For the purposes of this problem, use a cylindrical coordinate system such that the central axis of the solenoid is in the +z-direction, as shown coming out of the screen in the top illustration. The radial r-coordinate of each point is the distance to the central axis of the solenoid, and the angular ?-direction at each point is perpendicular both to the z-direction and to the r-direction as shown Assuming that the solenoid can be approximated as an infinitely long, tightly wound coil, which of the following are symmetries (or antisymmetries) of this system? symmetric under 180 rotations reversing the z-axis symmetric under rotations around the z-axis antisymmetric under 180° rotations around the z-axis symmetric under translations in the z-direction symmetric under translations in the r-direction end view antisymmetric under 180° rotations reversing the z-axis Scroll down for three more questions. side view Keening in mind the symmetries identified above, choose the best Amperian path to use for calculating the

Explanation / Answer

Answer:

2nd, 3rd and 5th options are correct.

It is because, even after rotation about z axis
or translation in z direction, the field will be in z axis only,
but if z axis is rotated, then obviously it will point towards -z now.

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