Answer to Question #172057 in Physics for Ashley

Question

One component of a magnetic field has a magnitude of 0.0427 T and points along the +x axis, while the other component has a magnitude of 0.0687 T and points along the -y axis. A particle carrying a charge of +1.31 × 10^-5 C is moving along the +z axis at a speed of 4.05 × 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.

Answer 1

a)

$$F_1=(1.31\cdot 10^{-5})(0.0427)(4.05\cdot 10^{3})\\=2.27\cdot 10^{-3}\ N\\ F_2=(1.31\cdot 10^{-5})(0.0687)(4.05\cdot 10^{3})\\=3.64\cdot 10^{-3}\ N$$

$$F=\sqrt{(2.27\cdot 10^{-3})^2+(3.64\cdot 10^{-3})^2}=4.3\cdot 10^{-3}\ N$$

b)

$$\theta=\arctan{\frac{2.27}{3.64}}=32\degree$$