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In a ring of current with radius [tex]r = 2.81 \, \text{cm}[/tex], if [tex]dl[/tex] covers 5.79 degrees of the ring, what is the length of the chunk of the ring (what is the length of [tex]dl[/tex])?

Answer :

The length of the chunk of the current ring (dl) is approximately 0.284 cm.

To find the length of the chunk of the current ring (dl), we need to use the formula:

[tex]dl = (Q/360) * 2\pi r[/tex]

Where Q is angle covered by dl, r is radius of the ring, and π is constant value (3.14159...).

Substituting the given values, we get:

[tex]dl = (5.799/360) * 2\pi (2.81 cm)[/tex]
dl = 0.0941 cm

Therefore, the length of the chunk of the ring (dl) is 0.0941 cm.

dl = r * θ

where
r = 2.81 cm (radius)
[tex]θ = Q * (\pi / 180)[/tex] (angle in radians)

Step 1: Convert angle from degrees to radians:
[tex]θ = 5.79° * (\pi / 180) = 0.101[/tex]radians (approx.)

Step 2: Calculate dl:
dl = 2.81 cm * 0.101 radians = 0.284 cm (approx.)

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