One component of a magnetic field has a magnitude of 0.046 T and points along the +x axis, while the other component has a magnitude of 0.066 T and points along the -y axis. A particle carrying a charge of +7.50*10^-5 C is moving along the +z axis at a speed of 3.20*10^3 m/s.
(a) What is the magnitude of the net magnetic force that acts on the particle?
(b) What is the angle that the net force makes with respect to the +x axis?
Use the magnetic force on a charge equation in two dimensions. If you need, use the right hand rule. I will be happy to critique your thinking.
I figured out the first question using F=Bqvsin90 for X anf Y and then used pythagorean theorem. But I have problems with b, how do I start going about finding the angle? thank you!
The angle with respect to the x axis?
The net force is in the xy plane, so
Theta= arc cos ( x component/magnitude)
To find the angle that the net force makes with respect to the +x axis, we can use the information about the components of the magnetic field.
The x-component of the magnetic field is given as 0.046 T and points along the +x axis, while the y-component is given as 0.066 T and points along the -y axis.
Since the net force is in the xy plane, we can represent it as the vector sum of the x and y components of the magnetic field.
Let's denote the x-component of the net force as Fx and the y-component as Fy. Then we have:
Fx = Bx * q * v * sin(theta_x)
Fy = By * q * v * sin(theta_y)
From the given information, we know that the particle is moving along the +z axis, so the angle between the velocity vector and the x-axis, theta_x, is 90 degrees. Similarly, the angle between the velocity vector and the y-axis, theta_y, is also 90 degrees.
Substituting these values, the equations become:
Fx = Bx * q * v * sin(90°) = Bx * q * v
Fy = By * q * v * sin(90°) = By * q * v
Now, to find the magnitude of the net magnetic force, we can use the Pythagorean theorem:
Magnitude of net force (F) = sqrt(Fx^2 + Fy^2)
For part (a), you mentioned that you've already found the magnitude of the net magnetic force by using the Pythagorean theorem, so you have that value already.
For part (b), to find the angle that the net force makes with respect to the +x axis, we can use the magnitude of the x-component, Fx, and the magnitude of the net force, F.
The angle, theta, can be found using the inverse cosine function:
Theta = arccos(Fx / F)
Substituting the values you already calculated, you can find the angle.