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.

B=sqrt{B(x)²+B(y)²} = …

F=qvBsinα
sinα=sin90=1 =>
F=qvB = …

To find the magnitude of the net magnetic force that acts on the particle, we can use the formula:

F = q(v x B)

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

a) First, let's find the vector product of v and B:

v x B = |v| |B| sin(theta) n

where |v| is the magnitude of velocity, |B| is the magnitude of the magnetic field, theta is the angle between v and B, and n is the unit vector perpendicular to the plane formed by v and B.

Since the particle is moving along the +z axis, the angle theta is 90 degrees, and sin(theta) equals 1. Therefore,

v x B = |v| |B| n

Now, let's calculate the magnitude of the net magnetic force:

F = q(v x B)

Given:
q = +1.01 × 10^-5 C (charge of the particle)
|v| = 4.18 × 10^3 m/s (magnitude of velocity)
|B| = 0.0445 T (magnitude of the magnetic field)

F = (+1.01 × 10^-5 C) (4.18 × 10^3 m/s) (0.0445 T)

Calculate the product: (+1.01 × 10^-5 C) (4.18 × 10^3 m/s) = 4.2178 × 10^-2 N

Now, multiply this by 0.0445 T:

F = (4.2178 × 10^-2 N) (0.0445 T)

Calculate the product: (4.2178 × 10^-2 N) (0.0445 T) = 1.880421 × 10^-3 N

Therefore, the magnitude of the net magnetic force that acts on the particle is approximately 1.880421 × 10^-3 N.

b) To determine the angle that the net force makes with respect to the +x axis, we can use trigonometry.

Let's call this angle phi.

tan(phi) = (By/Bx)

where By is the y-component of the magnetic field and Bx is the x-component of the magnetic field.

Given:
By = 0.0725 T
Bx = 0.0445 T

tan(phi) = (0.0725 T)/(0.0445 T)

Now, calculate the ratio: (0.0725 T)/(0.0445 T) ≈ 1.629

Therefore, the angle phi is approximately tan^(-1)(1.629), which is approximately 58.798 degrees.

Hence, the angle that the net force makes with respect to the +x axis is approximately 58.798 degrees.