Question

Two parallel wires separated by a distance of 10 cm carry currents of 10 A and 40 A along the same direction. Where should a third current be placed to experience no magnetic force?

• A. 2 cm from the 10 A current
• B. 8 cm from 10 A current
• C. 6 cm from 10 A current
• D. 5 cm from 10 A current

Hint:

Set the two fields equal between the wires: \(10/r = 40/(10-r)\); the null lies closer to the weaker current.

Answer 1

The Correct Option is A

Concept: A current-carrying wire experiences zero force only where the surrounding field is zero. The null lies nearer the weaker current, and between the wires since the currents are parallel.

Ratio method: The fields balance when the distances are in the ratio of the currents. With $r$ from the 10 A wire and $10-r$ from the 40 A wire,
\[\frac{r}{10-r} = \frac{I_{10}}{I_{40}} = \frac{10}{40} = \frac{1}{4}\]
So $4r = 10 - r$, giving $5r = 10$ and
\[\boxed{r = 2\ \text{cm from the 10 A wire}}\]
This sits closer to the smaller (10 A) current, exactly as expected for a field null.