- #1

wcjy

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- 10

- Homework Statement
- Consider 2 identical infinite current-carrying wires which runs along the X and Y axes

respectively. They carry identical currents I and the currents flow in the directions of the

axes. Find the net magnetic field (in vector form) at the coordinate (x, y, z) = (4,4,5).

- Relevant Equations
- Biot savar law

$$B = \frac {\mu_0 I}{2 \pi r} $$

By Right-hand Grip Rule, the direction of the magnetic field by wire in y-axis is into the paper (z)

while the direction of the magnetic field by wire in X-axis is upwards (+i)

The answer state the Magnetic field is in the (i - y) direction though.

Next calculating the magnitude,

Distance of point to the Y axis is $$\sqrt{4^2 + 4^2} = \sqrt{32}$$

Distance of point to the X axis is $$\sqrt{4^2 + 5^2} = \sqrt{41}$$

Therefore, Magnetic field = $$B = \frac {\mu_0 I}{2 \pi \sqrt{32}} +\frac {\mu_0 I}{2 \pi \sqrt{41}} $$

This will give some weird fraction which is wrong.

Correct answer is $$B = \frac {5\mu_0 I}{82 \pi } (\hat{i} - \hat{j}) $$

By Right-hand Grip Rule, the direction of the magnetic field by wire in y-axis is into the paper (z)

while the direction of the magnetic field by wire in X-axis is upwards (+i)

The answer state the Magnetic field is in the (i - y) direction though.

Next calculating the magnitude,

Distance of point to the Y axis is $$\sqrt{4^2 + 4^2} = \sqrt{32}$$

Distance of point to the X axis is $$\sqrt{4^2 + 5^2} = \sqrt{41}$$

Therefore, Magnetic field = $$B = \frac {\mu_0 I}{2 \pi \sqrt{32}} +\frac {\mu_0 I}{2 \pi \sqrt{41}} $$

This will give some weird fraction which is wrong.

Correct answer is $$B = \frac {5\mu_0 I}{82 \pi } (\hat{i} - \hat{j}) $$