Magnetic Field produced by moving charges

[shirobon]

Homework Statement

I have two related questions here.

1. A positive point charge is moving directly toward P. The magnetic field that the point charge produces at P is?

2. Two positive point charges move side by side in the same direction with the same velocity.
What is the direction of the magnitude of the force that the upper point charge exerts on the lower one?

Homework Equations

$$\vec{B} = \frac{μ_0}{4\pi} \frac{q\vec{v} \times \hat{r}}{r^2}$$

The Attempt at a Solution

For the first Question:
The correct answer is zero.
My answer is that is is perpendicular to the line from the point charge to the point P.
According to the right hand rule, the direction of the point charge is going to be the thumb, so the resulting magnetic field should be perpendicular to the velocity vector, in circles.
Like this

So why is the answer 0 and not perpendicular to the line, if the field is going around in a perpendicular plane?

For the second question:
The correct answer is toward the upper point charge (the force is attractive)

However, when I think about it conceptually, I imagine it like

So the magnetic field from one charge is repelling the other charge just as much as it is attracting.Could somebody point out where I went wrong? Thank you.

 

[BvU]

Hi Shirobon,

1. Note that P is directly ahead of the moving charge... mathematically the zero follows from $\vec v\times\vec r = 0$
Your end view is a plane straight through the moving charge; but you can see somehing has to change sign on the axis

2. I don't understand the book answer. Isn't it so that equal sign charges repel each other ? i.e. the force can not be attractive ?
Or does the exercise ask for the magnetic force only, and you forgot to tell us that? In that case:
I don't understand your reasoning: at the orange charge B is up and v is into the paper, so F is towards the red charge.
at the red charge B is down and v is into the paper, so F is towards the orange charge. What makes you state

So the magnetic field from one charge is repelling the other charge just as much as it is attracting.

?

 

[lychette]

Hi Shirobon,

1. Note that P is directly ahead of the moving charge... mathematically the zero follows from $\vec v\times\vec r = 0$
Your end view is a plane straight through the moving charge; but you can see somehing has to change sign on the axis

2. I don't understand the book answer. Isn't it so that equal sign charges repel each other ? i.e. the force can not be attractive ?
Or does the exercise ask for the magnetic force only, and you forgot to tell us that? In that case:
I don't understand your reasoning: at the orange charge B is up and v is into the paper, so F is towards the red charge.
at the red charge B is down and v is into the paper, so F is towards the orange charge. What makes you state
?

I agree with 2). If these were 2 wires carrying current in the direction shown then they would attract. The combined magnetic field 'wraps round' both wires.