Consider two current carrying coil of N turns and is of radius R, and they carry equal current I. If the two could are coaxial and their centers are x distance apart, the derive an expression for the magnitude of net magnetic field at point P, halfway between the coils. (a) Find the magnitude of the net magnetic field at point P. dB vanishes at point dx (b) Show that the first derivative of the magnetic field with respect to x, P. Why this is true? d² B (c) Show that the second derivative also vanishes at P, dx2 if x = R. What could this physically mean? R
Consider two current carrying coil of N turns and is of radius R, and they carry equal current I. If the two could are coaxial and their centers are x distance apart, the derive an expression for the magnitude of net magnetic field at point P, halfway between the coils. (a) Find the magnitude of the net magnetic field at point P. dB vanishes at point dx (b) Show that the first derivative of the magnetic field with respect to x, P. Why this is true? d² B (c) Show that the second derivative also vanishes at P, dx2 if x = R. What could this physically mean? R
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Transcribed Image Text:Consider two current carrying coil of N turns and is of radius R, and they carry equal current
I. If the two could are coaxial and their centers are x distance apart, the derive an expression
for the magnitude of net magnetic field at point P, halfway between the coils.
(a) Find the magnitude of the net magnetic field at point P.
dB
vanishes at point
dx
(b) Show that the first derivative of the magnetic field with respect to x,
P. Why this is true?
d² B
(c) Show that the second derivative also vanishes at P,
dx2
if x = R. What could this
physically mean?
R
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