Mapt Consider a long solenoid consisting of a coil of wire with radius R and n t

Question

Mapt Consider a long solenoid consisting of a coil of wire with radius R and n turns per unit length. The solenoid carries a current 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 sh 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 coming out of the screen in the 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 antisymmetric under 180° rotations reversing the z-axis symmetric under rotations around the z-axis symmetric under translations in the r-direction symmetric under translations in the z-direction antisymmetric under 180° rotations around the z-axis end view Scroll down for three more questions. side view Keeping in mind the symmetries identified above, choose the best Amperian path to use for calculating the magnetic field at a point inside the solenoid

Explanation / Answer

antisymmetric under 180 rotations reversing the z axis

symmetric under roations around the z-axis

symmetric under translations in r -direction

symmetric under translations in z -direction

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a rectangle in the rz plane , partially inside the solenoid

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from Amperian loop

B*L = uo*I*n*L

B = uo*n*I <<<<----ANSWER

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from right hand rule the magnetic is directed along positive z direction

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