Question

# A thin copper rod 1.0 m long has a mass of 0.050 kg and is ina magnectic field of 0.10 T. What minimum current in the rodis needed in order fot the magnetic force to cancel the weight ofthe rod?

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A thin copper rod 1.0 m long has a mass of 0.050 kg and is ina magnectic field of 0.10 T. What minimum current in the rodis needed in order fot the magnetic force to cancel the weight ofthe rod?

$$\displaystyle\sum{F}={m}{g}$$
$$\displaystyle{I}{L}{B}{\sin{\theta}}={m}{g}$$
$$\displaystyle{I}={\frac{{{m}{g}}}{{{L}{B}{\sin{\theta}}}}}$$
We need the minimum value of current (I) $$\displaystyle\therefore{L}{B}{\sin{\theta}}$$ to be the minimum value.
$$\displaystyle\therefore\theta={90}$$
$$\displaystyle{I}={\frac{{{m}{g}}}{{{L}{B}{\sin{{\left({90}\right)}}}}}}={\frac{{{m}{g}}}{{{L}{B}}}}={\frac{{{\left({0.050}\right)}{\left({9.80}\right)}}}{{{\left({1.00}\right)}{\left({0.10}\right)}}}}={4.9}{A}$$