Question
Two parallel wires seprated by a distance of 10cm carry currents of 10A and 40A along-the same direction. Where should a third current be placed so that it experiences no magnetic force?
✓
Answer
$\frac{\mu_010\text{i}}{2\pi\text{x}}=\frac{\mu_0\text{i}40}{2\pi(10-\text{x})}$$\Rightarrow\frac{10}{\text{x}}=\frac{40}{10-\text{x}}\Rightarrow\frac{1}{\text{x}}=\frac{4}{10-\text{x}}$
$\Rightarrow10-\text{x} = 4\text{x}$
$\Rightarrow5\text{x} = 10$
$\Rightarrow\text{x} = 2\text{cm}$
The third wire should be placed 2cm from the 10A wire and 8 cm from 40A wire.
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