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A long straight conductor carrying 1 A lies on a horizontal table. The horizontal component of the earth's field there is 3.0 × 10⁻⁵ T pointing south to north. When the current flows east to west, the force per unit length on the conductor is:
A6 × 10⁻⁵ N m⁻¹
BZero
C1.5 × 10⁻⁵ N m⁻¹
D3 × 10⁻⁵ N m⁻¹
Answer & Solution
Correct answer: D. 3 × 10⁻⁵ N m⁻¹
1. Force per unit length: $f = IB\sin\theta$.
2. The current (east–west) is perpendicular to the field (south–north), so $\theta = 90^\circ$, $\sin\theta = 1$.
3. Substitute $I = 1$ A, $B = 3.0\times10^{-5}$ T: $f = 1\times3.0\times10^{-5}$.
4. $f = 3\times10^{-5}$ N m⁻¹ (it would be zero only if current were along the field).
_Source: NCERT Class 12 Physics Ch 4 "Moving Charges and Magnetism", p.156_
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