Consider the following figure. (a) A conducting loop in the shape of a square of

Question

Consider the following figure.

(a) A conducting loop in the shape of a square of edge length ? = 0.420 m carries a current I = 10.8 A as in the figure above. Calculate the magnitude and direction of the magnetic field at the center of the square.

(b) If this conductor is reshaped to form a circular loop and carries the same current, what is the value of the magnetic field at the center?

magnitude in ?T? direction ? Consider the following figure. (a) A conducting loop in the shape of a square of edge length ? = 0.420 m carries a current I = 10.8 A as in the figure above. Calculate the magnitude and direction of the magnetic field at the center of the square. magnitude in A Mu T? direction ? (b) If this conductor is reshaped to form a circular loop and carries the same current, what is the value of the magnetic field at the center? magnitude in A Mu T? direction ?

Explanation / Answer

A)
Magnetic filed at the center of a square loop,

B = 2*sqrt(2)*mue*I/(pi*L)

= 2*sqrt(2)*4*pi*10^-7*10.8/(pi*0.42)

= 2.9*10^-5 T

= 29 micro T( in to the page)

B) If the conductor is reshaped to circular loop,

2*pi*r = 4*L

r = 2*L/pi

= 2*0.42/pi

= 0.267 m

at the center of a circular loop,

B = mue*I/(2*r)

= 4*pi*10^-7*10.8/(2*0.267)

= 2.54*10^-5 T

= 25.4 micro T( in to the apge)

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