One component of a magnetic field has a magnitude of 0.080 T and points along the +x axis, while the other component has a magnitude of 0.034 T and points along the -y axis. A particle carrying a charge of +1.00 10-5 C is moving along the +z axis at a speed of 3.60 103 m/s.
(a) What is the magnitude of the net magnetic force that acts on the particle?
N
(b) What is the angle that the net force makes with respect to the +x axis?
°
To calculate the magnitude of the net magnetic force acting on the particle, we can use the formula for the magnetic force on a charged particle moving in a magnetic field:
F = q * v * B * sin(θ)
Where:
F = magnitude of the net magnetic force
q = charge of the particle (+1.00 x 10^-5 C)
v = velocity of the particle (3.60 x 10^3 m/s)
B = magnitude of the magnetic field
In this case, we have two components of the magnetic field along the x-axis and y-axis respectively. To find the net magnetic field, we need to calculate the vector sum of these components using the Pythagorean theorem:
B_net = sqrt(Bx^2 + By^2)
Where:
Bx = magnitude of the magnetic field component along the x-axis (0.080 T)
By = magnitude of the magnetic field component along the y-axis (-0.034 T)
Let's calculate the magnitude of the net magnetic force (a):
B_net = sqrt((0.080 T)^2 + (-0.034 T)^2)
B_net = sqrt(0.0064 T^2 + 0.001156 T^2)
B_net = sqrt(0.007556 T^2)
B_net = 0.086 T
Now we can substitute this value of B_net along with the values of q, v, and B in the formula for the magnetic force to find F:
F = (1.00 x 10^-5 C) * (3.60 x 10^3 m/s) * (0.086 T) * sin(θ)
To find the angle (θ) that the net force makes with respect to the x-axis, we can use the equation:
θ = arctan(By / Bx)
θ = arctan(-0.034 T / 0.080 T)
Now let's calculate the values (a) and (b).