The field b = −2ax + 3ay + 4az mt is present in free space. find the vector force exerted on a straight wire carrying 12 a in the aab direction, given a(1, 1, 1) and:
(a) b(2, 1, 1);
(b) b(3, 5, 6).

The magnetic force on a current-carrying wire is given by:

F = iL×B

F = magnetic force, i = current, L = wire length vector, B = magnetic field

Note we are taking the cross product of the iL and B vectors, not the product of two scalars.

A) Given values:

i = 12A

L = AB = (2, 1, 1)m - (1, 1, 1)m = <1, 0, 0>

B = <-2, 3, 4>10⁻³T

Plug in and solve for F:

F = 12<1, 0, 0>×10⁻³<-2, 3, 4> = 10⁻³(<12, 0, 0>×<-2, 3, 4>)

Beware, we'll use array notation to show the cross product calculation:

F = 10⁻³

F = 10⁻³<(0)(4)-(0)(3), (0)(-2)-(12)(4), (12)(3)-(0)(-2)>

F = 10⁻³<0, -48, 36>N

B) Given values:

i = 12A

L = AB = (3, 5, 6)m - (1, 1, 1)m = <2, 4, 5>

B = <-2, 3, 4>10⁻³T

Plug in and solve for F:

F = 12<2, 4, 5>×10⁻³<-2, 3, 4> = 10⁻³(<24, 48, 60>×<-2, 3, 4>)

F = 10⁻³

F = 10⁻³<(48)(4)-(60)(3), (60)(-2)-(24)(4), (24)(3)-(48)(-2)>

F = 10⁻³<12, -216, 168>N

a high pressure system is a dense air mass that is usually cooler and drier than the surrounding air. a low pressure system is a less dense air mass that is usually wetter and warmer than the surrounding air.

in general, areas that experience high atmospheric pressure also experience fair weather. low pressure systems can cause the formation of clouds and storms. air usually flows from areas of high pressure to areas of low pressure..

real, smaller and upside-down.   so the answer should be b.