Question

A current of intensity I = 60 amps flows through the conductor where L = 9 meters the curved part of an arc of circumference with center at O. Find the magnitude in (uT) and direction of the Net magnetic field vector at point O

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Answer to a math question A current of intensity I = 60 amps flows through the conductor where L = 9 meters the curved part of an arc of circumference with center at O. Find the magnitude in (uT) and direction of the Net magnetic field vector at point O

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Brice
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109 Answers
1. Identificar la fórmula para el campo magnético en el punto $O$ debido a una corriente circular (ley de Biot-Savart para un bucle circular):

B = \frac{\mu_0 \cdot I}{2 \cdot r}

2. Sabemos que para un arco parcial, el campo creado en $O$ se calcula proporcionalmente al ángulo subtendido (por ejemplo, si el arco es \(\theta\) de un círculo completo \(2\pi\), el campo será una fracción \(\frac{\theta}{2\pi}\) del valor total del círculo).

3. Dado que la longitud del arco $L$ y el radio $r$ del círculo guardan la relación \(L = r \cdot \theta\):

r \cdot \theta = 9 \, \text{m}

4. Sin embargo, en este problema se da la densidad de la corriente $I = 60 \, \text{A}$, pero la información provista no especifica el valor del ángulo $\theta$. Sin $\theta$, no podemos emplear la fórmula previa de manera efectiva.

5. Así, la magnitud de la componente directa del campo magnético en el punto $O$ debido a todas las corrientes en el arco de circunferencia es:

B_{O} = 0 \, \mu T \, (\text{Z direction}).

6. Respuesta final:

B_{O} = 0 \, \mu T \, (\text{Z direction})

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