Question

Suppose we have an infinitely long wire carrying a current of 5.5 A. It is bent into an L-shape extending into positive infinities along the x- and y-axes. Find the magnitude of the magnetic field (in T) at a point P with coordinates (0.6 m, 0.6 m).

Answer 1

Answer:

The magnitude of the magnetic field at point T is $3.13\times 10^{- 6}\ T$

Solution:

As per the question:

Current, I = 5.5 A

From the figure shown:

$\theta = 45^{\circ}$

Now, the net magnetic field, B  at the point is given by:

Magnetic field due to one part of the wire,

$B = \frac{\mu_{o}I}{4\pi r}(sin\theta+ sin90^{\circ}) = \frac{\mu_{o}I}{4\pi r}(sin\theta + sin90^{\circ})$

$B' = 2\times B$

$B' = 2\times \frac{\mu_{o}I}{4\pi r}(sin45^{\circ} + sin90^{\circ})$

$B' = 2\times \frac{\mu_{o}I}{4\pi r}(\frac{1}{\sqrt{2}} + 1)$  

$B' = \frac{2\times 10^{- 7}\times 5.5}{0.6}(\frac{1}{\sqrt{2}} + 1)$  

$B' = 3.13\times 10^{- 6}\ T$