TPR Electrostatics Example 6-14

[ilovemcat]

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I don't understand how they solved this answer. Maybe you might.

Here's the question along with the solution:

Question: The electric field at a distance y above the center of a ring of charge is given by the formula E=kQy/(y² + R²)^³/², where Q is the charge on the ring and R is the radius.

If Q = +25 mC and R = 3 m, find the force that a charge q = +nC would feel if it were placed at y = 4 m.

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Their solution:

F = q x E
= q x (kQy/(y² + R²)^³/²)
= (25/9 x 10^-9 C) x (9 x 10^9 N-m²/C²] x (25 x 10^-³ C)(4 m) / [(4m)² + (3 m)² ]^³/²)
= (25 N-m²/C²)[(10^-1 C-m) / (5^³) m³]
= 2 x 10^-² N

It's not the calculations that bother me. I don't understand where, how, or why they got 25/9 for q. If someone could explain, it'd be really appreciated. Thanks!

 

[Phantastic]

You said the charge was +nC? like a positive nanocoloumb? Not sure why it's 25/9 but at least the 10^-9 makes sense...that should ballpark close enough right?

 

[ilovemcat]

You said the charge was +nC? like a positive nanocoloumb? Not sure why it's 25/9 but at least the 10^-9 makes sense...that should ballpark close enough right?

Yeah, positive nanocoloumb. Throughout my studying, I noticed TPR has made several calculation errors and I wasn't sure if this was one of them. I assumed it was just 1 x 10^-9 C as well. Just don't understand were the 25/9 came from.