QuestionJune 29, 2025

Calculate the force on a 160m wire carrying 150A of current if a magnetic field of 5times 10^-5 T makes a 165^circ angle with the wire. square N

Calculate the force on a 160m wire carrying 150A of current if a magnetic field of 5times 10^-5 T makes a 165^circ angle with the wire. square N
Calculate the force on a 160m wire carrying 150A of current if a magnetic field of 5times 10^-5 T makes a 165^circ angle with the wire. square N

Solution
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Answer

0.31056 N Explanation 1. Identify the formula for magnetic force The magnetic force on a current-carrying wire is given by **F = I \cdot L \cdot B \cdot \sin(\theta)**. 2. Substitute values into the formula Given: I = 150 \, \text{A}, L = 160 \, \text{m}, B = 5 \times 10^{-5} \, \text{T}, \theta = 165^\circ. Substitute these into the formula: F = 150 \cdot 160 \cdot 5 \times 10^{-5} \cdot \sin(165^\circ). 3. Calculate \sin(165^\circ) \sin(165^\circ) = \sin(180^\circ - 15^\circ) = \sin(15^\circ) \approx 0.2588. 4. Compute the force F = 150 \cdot 160 \cdot 5 \times 10^{-5} \cdot 0.2588 = 0.31056 \, \text{N}.

Explanation

1. Identify the formula for magnetic force<br /> The magnetic force on a current-carrying wire is given by **$F = I \cdot L \cdot B \cdot \sin(\theta)$**.<br /><br />2. Substitute values into the formula<br /> Given: $I = 150 \, \text{A}$, $L = 160 \, \text{m}$, $B = 5 \times 10^{-5} \, \text{T}$, $\theta = 165^\circ$. Substitute these into the formula: <br /> $F = 150 \cdot 160 \cdot 5 \times 10^{-5} \cdot \sin(165^\circ)$.<br /><br />3. Calculate $\sin(165^\circ)$<br /> $\sin(165^\circ) = \sin(180^\circ - 15^\circ) = \sin(15^\circ) \approx 0.2588$.<br /><br />4. Compute the force<br /> $F = 150 \cdot 160 \cdot 5 \times 10^{-5} \cdot 0.2588 = 0.31056 \, \text{N}$.
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