Question

An alpha particle (carrying a positive charge q = 3.2 × 10^-19 C) enters a region of uniform 

magnetic field of induction

\(\vec B\) = (0.5\(\hat i\) + \(\hat j\) - \(\hat k\)) T with a velocity

\(\vec v\) = (4\(\hat i\) + 4\(\hat j\) + \(\hat k\)) x 10² m/s. 

What is the force \(\vec F\) on the alpha particle?

Answer 1

Data : q = 3.2 x 10^-19C, \(\vec B\) +  = (0.5\(\hat i\) + \(\hat j\) - \(\hat k\)) T,

\(\vec v\) = (4\(\hat i\) + 4\(\hat j\) + \(\hat k\)) x 10² m/s

The force on the alpha particle

\(\vec F\) = q \(\vec v\) x \(\vec B\)

= (3.2^-19 C) [(4\(\hat i\) + 4\(\hat j\) + \(\hat k\)) x 10² m/s] x [(0.5\(\hat i\) + \(\hat j\) - \(\hat k\)) T]