# 3x3 Matrix (Lorentz force law)- determinant

• Oct 11th 2012, 04:15 AM
froodles01
3x3 Matrix (Lorentz force law)- determinant
Using the Lorentz force law for my problem, I get the following matrix.

I ex ey ez I
I 1 . -1 . 0 I
I 1 . 0 . -1 I

I have evaluated the ey term as a -ve ( ey((1X-1)-(0x1)) = ey(-1-0) = -1ey)

= ex((-1x-1)-(0x0)) + ey((1X-1)-(0x1)) + ez ((1x0)-(-1x1))
= ex - ey + ez

Another person evaluates this term as +ve. so could someone point out the obvious mistake I made, please, I can't see it.

The set problem is
An electron in a magnetic field B=2.0T(ex-ez) has velocity v=(2.5x107 ms-1 (ex-ey)
a) calculate magnetic force on electron at that instant
Now, F = -e 2(2.5x107) (ex-ez)* (ex-ey)

so
F = -8x10-12 (ex - ey + ez)
• Oct 11th 2012, 06:16 AM
HallsofIvy
Re: 3x3 Matrix (Lorentz force law)- determinant
You have done the cross product incorrectly. The j coefficient is the negative of the minor.
• Oct 11th 2012, 06:47 AM
froodles01
Re: 3x3 Matrix (Lorentz force law)- determinant
AH! . . . . . I WAS missing something after all.
Ta!
• Oct 11th 2012, 12:26 PM
HallsofIvy
Re: 3x3 Matrix (Lorentz force law)- determinant
The cross product of vectors <a, b, c> and <p, q, r> is
$\left|\begin{array}{ccc}i & j & k \\ a & b & c \\ p & q & r\end{array}\right|$
expanding that on the first row it is
(br- cq)i- (ar- cp)j+ (aq- bp)k.