A current Is set up In a wire loop consisting of a semlcircle of radius 4.01 cm,

Question

A current Is set up In a wire loop consisting of a semlcircle of radius 4.01 cm, a smaller concentric semicircle. and two radial straight lengths, aim the same Figure snows the arrangement but Is not drawn to scale. The magnitude of the magnetic field produced at the center of curvature Is 47.49 j/T. The smaller is then flipped over (rotated) until the loop Is again entirety in the same plane (Figure (&)). The magretlc field produced at the (same) center of curvature now has magnitude 15.83 muT, and Its direction is reversed what is the radius of the smaller aemtcircle?

Explanation / Answer

Here,

let the current in the loop is I

radius of smaller loop is a

radius of larger loop , b = 4.01 cm = 0.0401 m

for figure a)

Ba = u0*I/(4) * (1/a + 1/b)

47.49 *10^-6 = 4pi *10^-7* I/(4) * (1/0.0401 + 1/a) ---(1)

for the figure b

Bb = u0*I/(4) * (1/a - 1/b)

15.83 *10^-6 = 4pi *10^-7* I/(4) * (- 1/0.0401 + 1/a) -----(2)

From 1 and 2

47.49 *10^-6/(15.83 *10^-6 ) = 4pi *10^-7/(4) * (1/0.0401 + 1/a) /(4pi *10^-7/(4) * (- 1/0.0401 + 1/a))

solving for a

a = 0.0201 m = 2.01 cm

the radius of smaller loop is 2.01 cm

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