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The horizontal component of the earth’s magnetic field at a certain place is 3.0×10⁻⁵ T and the direction of the field is from the geographic south to the geographic north. A very long straight conductor is carrying a steady current of 2 A. What is the force per unit length on it when it is placed on a horizontal table and the direction of the current is east to west?

Asked in GUJCET 2021 · Force on a wire in a field

• (1) 3×10⁻⁵ N m⁻¹
• (2) 9×10⁻⁵ N m⁻¹
• (3) 6×10⁻⁵ N m⁻¹
• (4) 2×10⁻⁵ N m⁻¹

Step-by-step solution

Why the other options are wrong

• (1) 3×10⁻⁵ is the field itself, in tesla. It would be the answer for a 1 A current; with 2 A flowing, F/ℓ=BI still needs that second factor.
• (2) 9×10⁻⁵ multiplies the field by 3 — the 3.0 of the field value used again as a current. The current in the stem is 2 A.
• (4) 2×10⁻⁵ is the current wearing the field's power of ten. F/ℓ=BI needs both numbers, 3.0×10⁻⁵ and 2.

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