Question

A current is flowing in a wire in direction 3i + 4j where the direction of the magnetic field is 5j + 12k. The force on the wire is:_____

a. 0.71(i + j).
b. 0.78i - 0.58j + 0.24k.
c. 0.78i + 0.58j - 0.24k.
d. 0.78i + 0.58j + 0.24k.

Answer 1

F = 0.768 i ^ - 0.576 j ^ + 0.24 k ^

the correct answer is "b"

Step-by-step explanation:

The magnetic force is

F = i l x B

The bold are vectors, in this case they give us the direction of the current and the magnetic field, for which we can solve as a determinant

`F = i \left[\begin{array}{ccc}x&y&z\\3&4&0\\0&5&12\end{array}\right]`

resolver

F = i ^ (4 12 - 0) + j ^ (0- 3 12) + k ^ (3 5 - 0)

F = i (48 i ^ - 36 j ^ + 15 k⁾

in this case i is the value of the current flowing through the cable

i = 16 mA = 0.016 A

F = 0.768 i ^ - 0.576 j ^ + 0.24 k ^

When reviewing the different answers, the correct answer is "b"