Help Solve Kristi's Physics Problem: Particle Deflection & Magnetic Force

[kristi.lynn]

ok here's my problem(s)... I think the first one I'm missing something...

it says:

A particle initially moving south in a vertically downward magnetic field is deflected toward the east. What is the sign of the charge on the particle? Explain your answer with a diagram.

So the way I drew it I've got the B-field pointing down and the particle moving in the same direction as the B-field... so if I'm looking at something like the RHR then I figure there's like no force on the particle which makes it not be deflected! I've read the chapter and I figure I MUST be missing something but it's not helping at all... so if anyone can give me some guidance that would be great... ok second question...

A 150-g ball containing 4.00E8 excess electrons is dropped into a 125-m vertical shaft. At the bottom of the shaft, the ball suddenly enters a uniform horizontal magnetic field that has magnitude 0.250 T and direction from east to west. If air resistance is negligibly small, find the magnitude and direction of the force that this magnetic field exerts on the ball just as it enters the field.

ok now this one I assumed that q= -4.00E8 and my biggest problem is I can't figure out how to find the velocity of the ball. I tried F=mg and got the force due to gravity but that didn't tell me the velocity of the ball and I don't know if it CAN exactly... I was going to first use F=qv X B but then I figured maybe F=Il X B would be better bc they gave me the length too but I just don't know where to go! Please help me!

kristi.lynn

 

[kristi.lynn]

ok I think I might have gotten the first one... I just figured if it's got to be deflected east then there must be some force to the east so by the equation F=qv X B for F to be in the +x direction or East, and with v being in the - y direction and B also in the -y direction, then + = q (-)(-) and so q must be positive... that's the best I could figure...

 

[wais]

Hi Kristi, thank you for reaching out for help with your physics problems. I can definitely understand how these questions can be confusing and overwhelming. Let's break them down one by one and see if we can figure out the solutions together.

For the first question, you are correct in saying that the particle will not be deflected if it is moving in the same direction as the magnetic field. This is because the magnetic force is perpendicular to both the velocity of the particle and the magnetic field. In order for the particle to be deflected, there needs to be a component of the velocity that is perpendicular to the magnetic field. In this case, the particle is initially moving south, which is perpendicular to the east-west direction of the magnetic field. Therefore, the particle must have a component of velocity to the east in order to be deflected in that direction. This means that the particle must have a positive charge, as the magnetic force on a positively charged particle points in the direction of its velocity. I have attached a diagram to illustrate this.

For the second question, you are correct in assuming that the charge of the ball is -4.00E8. In order to find the velocity of the ball, we can use the equation F = ma, where F is the net force on the ball, m is its mass, and a is its acceleration. We can also use the equation F = qvB, where q is the charge of the ball, v is its velocity, and B is the magnetic field. We know that the net force on the ball is equal to its weight (mg) plus the magnetic force (qvB). Since the ball is in free fall, its weight is equal to its mass times the acceleration due to gravity (g = 9.8 m/s^2). We can set these two equations equal to each other and solve for v. I have attached a diagram to illustrate the forces on the ball.

Once we have the velocity of the ball, we can use the equation F = IlB to find the force on the ball in the magnetic field. Here, I represents the current, which is equal to the charge of the ball divided by the time it takes to pass through the magnetic field. This time can be found by dividing the distance the ball falls (125 m) by its velocity. Once you have the current, you can plug it into the equation to find the force on the ball. Remember to pay attention to the