# Physics - Magnetic Fields?

An electron is traveling at a velocity of v = (1.2x10^6 m/s i-hat) + (0.8x10^6 m/s j-hat). At a point in space, the electron travels through a magnetic field of (0.2 T i-hat + 0.08 k-hat). What is the magnetic force acting on the electron?

Relevance

I'll use a slightly different convention:

v = (1.2e6, 0.8e6, 0) m/s

to show the i, j, and k components

and by the same convention

B = (0.2, 0, 0.08) T

That's simply the data you gave in another format I find easier to work with in this text-based forum. Good so far?

You (should) know that

F = q*v ₓ B

where F, v and B are vectors

and ₓ represents the cross product

v ₓ B = (1.2e6, 0.8e6, 0) ₓ (0.2, 0, 0.08) T·m/s

v ₓ B = (64000, -96000, -160000) N/C

Multiply that product by the charge -1.6e-19 C and you get

F = (-1.0e-14, 1.5e-14, 2.6e-14) N

I've rounded to two significant digits, but the data actually supports only one.

I usually use wolframalpha for my cross products; see citation below.

• given

v = 1.2 X 106 i + 0.8 X 106 j

B = 0.2 T i + 0.08 T k

q = 1.6 X 10-19 C

we have equation

F = q ( v X B )

= 1.6 X 10-19 X ( v X B )

| i j k |

( v X B ) = | 1.2 X 106 0.8 X 106 0 |

| 0.2 0 0.08 |

= i ( 800000 X 0.08 - 0 X 0 ) - j ( 1200000 X 0.08 - 0 X 0.2 ) + k ( 1200000 X 0 - 800000 X 0.2 )

= i ( 64000 - 0 ) - j ( 96000 - 0 ) + k ( 0 - 160000 )

= i ( 64000 ) - j ( 96000 ) - k ( 160000 )

= 1.6 X 10-19 X i ( 64000 ) - j ( 96000 ) - k ( 160000 )

FB = 1.02 X 10-14 i - 1.536 X 10-14 j - 2.56 X 10-14 k