Physics GRE GR 1777, Problem 020 Solution

20. Electrodynamics (Magnetic field)

Solution
The magnitude of the magnetic field can be obtained from the Biot-Savart law.

B = \frac{ \mu_0 I }{ 4\pi R^2} \oint dL
where R is the radius of the loop and I is the current. In this problem, the radius of the circular loop is a, the magnitude of the magnetic field at the center of a circular loop is
B = \frac{ \mu_0 I }{ 4\pi a^2} \cdot (2\pi a) = \frac{ \mu_0 I }{ 2a }

Answer
(D) \frac{ \mu_0 I }{ 2a } 
Reference
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html

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