Mathematics

Problem

A straight aluminium rod of length

0.30\,\text{m}

and cross-sectional area

2.0\times10^{-6}\,\text{m}^2

is held horizontally by two light vertical threads in air. The density of aluminium is

2.7\times10^{3}\,\text{kg m}^{-3}

. The entire arrangement is placed in a uniform magnetic field of

0.25\,\text{T}

directed vertically downward. A current is passed through the rod from west to east. (a) Calculate the current that will make the tensions in the threads zero. (b) If the current is increased to

1.5

times this value, state the magnitude and direction (upward or downward) of the net force acting on the rod.

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