Magnetic Field of a point charge

[majormaaz]

Homework Statement

A point charge q = -2.9 μC moves along the z-axis with a velocity v^→ = (+7.3 x 10⁵ m/s) k . At the moment it passes the origin, what are the strength and direction of the magnetic field at the following positions? Express each field vector in Cartesian form.

(a) At position r₁ = (2.0 cm, 0 cm, 0 cm)
(b) At position r₂ = (0 cm, 4.0 cm, 0 cm).
(c) At position r₃ = (0 cm, 0 cm 1.5 cm).
(d) At position r₄ = (3.5 cm, 1.5 cm, 0 cm).
(e) At position r₅ = (3.0 cm, 0 cm, 1.0 cm)

Homework Equations

B_{point charge} = [μ₀/4pi] * [qv x sin Θ / r²]

The Attempt at a Solution

I saw that this problem has a negative charge, so I'd have to use the RHR and reverse direction to account for the charge being negative. I also got the fact that the magnetic field at a point along the same axis as the charge's velocity is 0 Teslas.

I ended up with
(a) 0 i + _ j + 0 k
(b) _ i + 0 j + 0 k
(c) 0 i + 0 j + 0 k
(d) _ i + _ j + 0 k
(e) 0 i + _ j + 0 k

However, everytime I used the point charge formula I have, I end up with an incorrect answer. For example, in part (a), with a r = 2 cm = 0.02 m, I plugged that into [μ₀/4pi] * [|q|v x sin Θ / r²], and then reversing the sign to account for a negative charge, but it didn't work.
i.e. I calculated that for part (a), a value of 2 cm for r would have a magnetic field of -5.29e-4 T in the j direction, but that's apparently not right.

 

[Simon Bridge]

I calculated that for part (a), a value of 2 cm for r would have a magnetic field of -5.29e-4 T in the j direction, but that's apparently not right.

What makes you think that is not right?

$$\vec B = \frac{\mu_0}{4\pi}\frac{q\vec v\times \vec r}{r^3}$$

For part a: $\vec v = (0,0,v)^t,\;\vec r = (x,0,0)^t$
$$\vec B = \frac{\mu_0q}{4\pi x^3}\left|\begin{matrix}\hat\imath & \hat\jmath & \hat k\\ 0 & 0 & v\\ x & 0 & 0\end{matrix}\right| = \frac{\mu_0 qv}{4\pi x^2}\hat\jmath$$... plug the numbers in and show me your working.

ref: http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html