Question

A proton moves with a velocity of vector v = (6i hat bold - 3j hat bold + k hat bold) m/s in a region in which the magnetic field is vector B = (i hat bold + 2j hat bold - 3k hat bold) T. What is the magnitude of the magnetic force this charge experiences? N

Answer 1

v=(6i-3j+k) m/s
B=(i+2j-3k) T
F=e[v,B]
i j k
x₁ y₁ z₁ =
x₂ y₂ z₂

i j k
6 -3 1 =
1 2 -3
=(y₁z₂-z₁y₂)i +(z₁x₂-x₁z₂)j +(x₁y₂-y₁x₂)k=
=(7i+19j+15k).

|[v,B] |=sqrt{7²+19²+15²}=25.2
F= 1.6•10⁻¹⁹•25.2=4.03•10⁻¹⁸ J.