A square loop made of copper wire is falling out of a region where there is a ma

Question

A square loop made of copper wire is falling out of a region where there is a magnetic field B_ext = 0.10 T. The loop is falling with a constant velocity because of the current induced in the loop. What is the velocity of the loop? Give your answer in m/s to at least three significant digits to avoid being counted wrong for rounding. It will be useful to know that: The mass density of copper (mass per volume) is 9.0 times 10^3 kg/m^3. The volume of the wire is A L, where A is the cross-sectional area of the wire and L is the total length (sum of the length of the four sides). The resistivity of copper is p = 1.7 times 10^-8 Ohm-m. The resistance of the wire is R = p L/A, where A and L are again the cross-sectional area and length of the wire.

Explanation / Answer

Here ,

let the current in the wire is I

as I = B*v*l/R

R = 1.7 *10^-8 * L/A

as F = m * g = B *I*l

B*v*L/R = m * g

B^2 * v *(L/4)^2/(1.7 *10^-8 * L/A) = 9 *10^3 * L * A * g

0.10^2 * v *(L/4)^2/(1.7 *10^-8 * L/A) = 9 *10^3 * L * A * 9.80

solving for v

v = 2.4 m/s

the speed of the loop is 2.4 m/s

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