# Find loop radius and current via magnetic field?

#### jlmccart03

1. Homework Statement
A single-turn wire loop produces a magnetic field of 41.2 μT at its center, and 5.15 nT on its axis, at 20.0 cm from the loop center.

Find loop raidus and current.

2. Homework Equations
F = qv x B

3. The Attempt at a Solution
I tried to use the above equation, but could not figure out how to use it to find a radius r. What must be done in order to get an equation with such variables? For current I believe F = IL x B should work, but I don't know if radius r is necessary.

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#### kuruman

Homework Helper
Gold Member
Sounds like you need to use Biot-Savart to find a general expression for the B-field on the loop axis at distance z from the center, then solve a system of 2 equations and two unknowns.

#### jlmccart03

Sounds like you need to use Biot-Savart to find a general expression for the B-field on the loop axis at distance z from the center, then solve a system of 2 equations and two unknowns.
So I need to use the equation dB = (μ0IdL × Ir)/(4πr2) and solve for r?

Homework Helper
Gold Member

#### jlmccart03

Yes, but you need to integrate first. Read and understand the derivation for $B_z$ here.
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html
Then use this expression for the two values of $z$ that are given to you. You need to solve for both the current and the radius.
So what z value do I plug in? Also what would be my I? I am confused on how to use this equation. I guess a better question to ask is what does each value correspond to? I am looking at the derivation and am simply confused because this creates a trianlge as far as the diagram shows, but how does this relate to my problem?

#### kuruman

Homework Helper
Gold Member
Forget the derivation and plugging in for the moment. Read the statement of the problem carefully. This loop produces a magnetic field everywhere in space around it. Can you explain to me what you think the given numbers represent? (Fill in the blanks)
Using the coordinate axes in the hyperphysics derivation,
(a) 41.2 μT is the magnetic field at point x = ____, y = ____ , z = ____
(b) 5.15 nT is the magnetic field at point x = ____, y = ____ , z = ____
(c) 20.0 cm is the distance from point x = ____, y = ____ , z = ____ to point x = ____, y = ____ , z = ____.

"Find loop radius and current via magnetic field?"

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