You have a 1.0-m-long copper wire. You want to make an N-turn current loop that generates a 1.0 mT magnetic field at the center when the current is 1.0 A. You must use the entire wire. What will be the diameter of your coil?
The total length of the copper wire is , the current through the wire is and the magnetic field at the center of the coil is .
The formula to calculate the total length of the wire can be written as
Here, is the total length of the wire, i the number of turns when the wire is bent into a circular loop and is the diameter of the loop.
Simplify equation (1) to obtain the number of turns in the loop.
The formula to calculate the magnetic field at the center of a circular loop is given by
Here, is the magnetic field, is the permeability of free space and is the current through the loop.
Substitute the expression for the number of turns from equation (2) into equation (3) and simplify to obtain the diameter of the loop.
Substitute for , for , for and for into equation (4) to calculate the required diameter.
The required diameter of the loop is .
The coaxial cable shown in consists of a solid inner conductor of radius surrounded by a hollow, very thin outer conductor of radius . The two carry equal currents I, but in opposite directions. The current density is uniformly distributed over each conductor.
a. Find expressions for three magnetic fields: within the inner conductor, in the space between the conductors, and outside the outer conductor.
A conducting bar of length l and mass m rests at the left end of the two frictionless rails of length d in FIGURE P29.75. A uniform magnetic field of strength B points upward.
a. In which direction, into or out of the page, will a current through the conducting bar cause the bar to experience a force
to the right?
b. Find an expression for the bar’s speed as it leaves the rails at
the right end.
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