Concept:A straight wire carrying an electric current through a uniform external magnetic field experiences a macroscopic Lorentz force.
Formula:$$ F = ILB \sin(\theta) $$
Solution:- First, convert all units to standard SI units: The length \( L = 100 \ \text{cm} = 1.0 \ \text{m} \).
- Identify the other givens: Magnetic field \( B = 0.5 \ \text{T} \), Current \( I = 10 \ \text{A} \).
- Determine the angle: The problem states the wire is "perpendicular" to the field, so \( \theta = 90^\circ \), and \( \sin(90^\circ) = 1 \).
- Calculate the force: \( F = (10)(1.0)(0.5)(1) \).
- \( F = 5 \ \text{N} \).
Why other options are incorrect:Option D occurs if one forgets to convert centimeters to meters, resulting in \( 10 \times 100 \times 0.5 = 500 \) or similar scaling errors. Options A and B are simple math errors.
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