# Magnetic Field of a point charge

**1. The problem statement, all variables and given/known data**

A point charge q = -2.9 μC moves along the z-axis with a velocity v

^{→}= (+7.3 x 10

^{5}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 r_{1} = (2.0 cm, 0 cm, 0 cm)

(b) At position r_{2} = (0 cm, 4.0 cm, 0 cm).

(c) At position r_{3} = (0 cm, 0 cm 1.5 cm).

(d) At position r_{4} = (3.5 cm, 1.5 cm, 0 cm).

(e) At position r_{5} = (3.0 cm, 0 cm, 1.0 cm)

**2. Relevant equations**

B_{point charge} = [μ_{0}/4pi] * [qv x sin Θ / r^{2}]

**3. 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 [μ_{0}/4pi] * [|q|v x sin Θ / r^{2}], 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.

http://ift.tt/1jkiYLP

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