Question

A wire 73.6 cm long carries a 0.720 A current in the positive direction of an x axis through a magnetic field with an x component of zero, a y component of 0.000270 T, and a z component of 0.00770 T. Find the (a) x, (b) y, and (c) z components of the magnetic force on the wire.

Answer 1

(a)

0

(b)

- 0.0041

(c)

0.000143

Step-by-step explanation:

`\underset{L}{\rightarrow}` = length of the long wire = 73.6 cm = 0.736
`\hat{i}` m

`\underset{B}{\rightarrow}` = magnetic field = 0
`\hat{i}` + 0.000270
`\hat{j}` + 0.00770
`\hat{k}`

i = current in the wire = 0.720 A

Magnetic force is given as

`\underset{F}{\rightarrow}` = i (
`\underset{L}{\rightarrow}` x
`\underset{B}{\rightarrow}`)

Inserting the values

`\underset{F}{\rightarrow}` = (0.720) ((0.736
`\hat{i}`) x (0
`\hat{i}` + 0.000270
`\hat{j}` + 0.00770
`\hat{k}`))

`\underset{F}{\rightarrow}` = (0.720) (0
`\hat{i}` - 0.0056672
`\hat{j}` + 0.00019872
`\hat{k}`)

`\underset{F}{\rightarrow}` = 0
`\hat{i}` - 0.0041
`\hat{j}` + 0.000143
`\hat{k}`

(a)

x- component = 0

(b)

y-component = - 0.0041

(c)

z-component = 0.000143