One component of a magnetic field has a magnitude of 0.0445 T and points along the +x axis, while the other component has a magnitude of 0.0725 T and points along the -y axis. A particle carrying a charge of +1.01 × 10-5 C is moving along the +z axis at a speed of 4.18 × 103 m/s. (a) Find the magnitude of the net magnetic force that acts on the particle. (b) Determine the angle that the net force makes with respect to the +x axis.

To find the magnitude of the net magnetic force acting on the particle, we can use the equation for the magnetic force experienced by a charged particle moving through a magnetic field:

F = qvBsinθ

where F is the magnetic force, q is the charge of the particle, v is the velocity, B is the magnetic field, and θ is the angle between the velocity vector and the magnetic field vector.

In this case, the particle is moving along the +z axis, so the velocity vector is in the +z direction. We are given the charge of the particle, q = +1.01 × 10^-5 C, and the speed of the particle, v = 4.18 × 10^3 m/s.

We need to find the net magnetic field vector first. The magnetic field has two components: one along the +x axis and the other along the -y axis. The x-axis component is Bx = 0.0445 T, and the y-axis component is By = -0.0725 T.

To get the net magnetic field vector, we need to add these two components using vector addition.

Bnet = √((Bx)^2 + (By)^2)

Bnet = √((0.0445 T)^2 + (-0.0725 T)^2)

Bnet = √(0.00198 T^2 + 0.00526 T^2)

Bnet = √0.00724 T^2

Bnet = 0.085 T (approx)

Now, we can calculate the magnitude of the net magnetic force using the equation mentioned earlier:

F = qvBnet sinθ

Since the particle is moving along the +z axis, the angle between the velocity vector and the magnetic field vector is 90 degrees.

Therefore, sinθ = sin(90°) = 1

F = (1.01 × 10^-5 C)(4.18 × 10^3 m/s)(0.085 T)(1)

F ≈ 3.62 × 10^-2 N

Thus, the magnitude of the net magnetic force acting on the particle is approximately 3.62 × 10^-2 N.

Now, let's determine the angle that the net force makes with respect to the +x axis.

Since the net magnetic field has components along the +x axis and the -y axis, the net magnetic force will have components along the same directions.

Let the angle between the net magnetic force and the +x axis be θf.

Using the components of the net magnetic force, we can write:

Fx = Fcosθf
Fy = -Fsinθf

Since F = 3.62 × 10^-2 N, we can calculate the components of the force:

Fx = 3.62 × 10^-2 N * cosθf
Fy = -3.62 × 10^-2 N * sinθf

Now, we can find the tangent of the angle:

tanθf = -Fy / Fx

θf = tan^(-1)(-Fy / Fx)

Plug in the values:

θf = tan^(-1)(-(3.62 × 10^-2 N * sinθf) / (3.62 × 10^-2 N * cosθf))

After solving this equation, we can find that the angle the net force makes with respect to the +x axis is approximately 135 degrees.