Long straight wire: Ampere/Biot Savart

[Roodles01]

Homework Statement

A long straight wire carries a current of 2.0A. An electron moves parallel to it at a distance of 0.01m (I'm assuming id doesn't matter which way it moves) at a velocity, v = 100ms^-1
Calculate magnitude & direction of force acting on it.

Homework Equations

B = μ₀ L / 2∏r

F = q(v X B)

I know the second is the Lorentz force law & that the first relates to Biot-Savart but for the Biot-Savart I also have,
F₁₂ = μ0/4∏ * I₁ δl₁ * ( I₂ δl₂ * rhat ₁₂) / r₁₂²

So how does one relate to the other, please.

The Attempt at a Solution

Surely it can't be this easy!

B = μ₀ L / 2∏r
B = 4∏x10^-7 * 2.0 / 2∏(0.01)
B = 3.95x10^-8 T

F = q(v X B)
F = (-1.6x10^-19)(100x10³)(3.95x10^-8
F = -6.32x10^-22 N

Magnitude 6.32x10^-22 N
Direction (radially) away from wire

 

[rude man]

Homework Statement

A long straight wire carries a current of 2.0A. An electron moves parallel to it at a distance of 0.01m (I'm assuming id doesn't matter which way it moves) at a velocity, v = 100ms^-1
Calculate magnitude & direction of force acting on it.


Surely it can't be this easy!

B = μ₀ L / 2∏r
B = 4∏x10^-7 * 2.0 / 2∏(0.01)
B = 3.95x10^-8 T

F = q(v X B)
F = (-1.6x10^-19)(100x10³)(3.95x10^-8
F = -6.32x10^-22 N

Magnitude 6.32x10^-22 N
Direction (radially) away from wire

Surely it can!
Except the direction could be towards or away from the wire, depending on the relative direction of v and i and the position of q.

BTW I've never seen L used for current before ...

 

[Roodles01]

L . . . oops!