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

Answer:

(a)

0

(b)

- 0.0041

(c)

0.000143

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