# The attached figure shows a wire consisting of 4 straight-line segments connecting the points (0,1) → (1,0) → (2,3) → (4,−3) → (6,−1) all measured in meters A current of I=2 A flows...

The attached figure shows a wire consisting of 4 straight-line segments connecting the points (0,1) → (1,0) → (2,3) → (4,−3) → (6,−1) all measured in meters

A current of I=2 A flows along this wire from the point (0,1) to the point (6,−1).

If a constant external magnetic field B = (9i+ 3j− 4k) T exists, determine the magnitude of the total magnetic force on this wire.

a - 55 N

b - 66 N

c - 77 N

d - 88 N

e - 99 N

f - None

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### 2 Answers

The magnetic force on length L of a wire carrying a current I due to a magnetic field B is equal to `F = I*LxxB` .

In the problem, the wire carries a current 2 A. The magnetic field is (9i + 3j- 4k) T.

The magnetic force on the segment from (0, 1) to (1, 0) is equal to `2*(i - j)xx(9i + 3j- 4k)` = 8i + 8j + 24k

The magnetic force on the segment from (1,0) to (2, 3) is equal to `2*(i + 3j)xx(9i + 3j- 4k)` = -24i + 8j - 48k

The magnetic force on the segment from (2,3) to (4, -3) is equal to `2*(2i - 6j)xx(9i + 3j- 4k)` = 48i + 16j + 120k

The magnetic force on the segment from (4,-3) to (6, -1) is equal to `2*(2i +2 )xx(9i + 3j- 4k)` = -16i + 16j - 24k

The sum of the force on all the segments is 16i + 48j +72k

The magnitude of force is 88 N

**Sources:**

Can you explain how you get from 16i + 48j +72k to the answer of 88N?