Question

An electron moves with velocity v⃗ =(5.8i−6.7j)×104m/s in a magnetic field B⃗ =(−0.81i+0.60j)T.

Determine the x-component of the force on the electron.

Determine the y-component of the force on the electron.

Determine the z-component of the force on the electron.

Answer 1

Fₓ = 0,
`F_(y)` = 0 and
`F_(z)` = - 3.115 10⁻¹⁵ N

Step-by-step explanation:

The magnetic force given by the expression

F = q v xB

the bold are vectors, the easiest analytical way to determine this force in solving the determinant

`F = q \left[\begin{array}{ccc}i&j&k\\5.8&-6.7&0\\-0.81&0.6&0\end{array}\right] 10^(4)`

F = 1.6 10⁻¹⁵ [ i( 0-0) + j (0-0) + k^( 5.8 0.60 - 0.81 67) ]

F =i^0 + j^0 - k^ 3.115 10⁻¹⁵ N

Fₓ = 0

`F_(y)` = 0

`F_(z)` = - 3.115 10⁻¹⁵ N