Physics, asked by mishraj2001, 1 year ago

State biot savart law and apply it to find the magnetic field due to a circular loop carrying current at a point a) at its centre b) on the axis

Answers

Answered by nitkumkumar
30

Biot Savart Law

Biot Savart Law is an equation that describes the magnetic field created by a current carrying wire and allows us to calculate its strength at various points .

According to Biot Savart Law , the magnetic field produced by infinitesimal length of conductor is given by -

dB = \frac{uo * I * dL X 1r}{4\pi r^{2} }

where, dL = infinitesimal length of conductor carrying current

           1r  = unit vector directing from current to field point.

Magnetic field at centre of loop

According to Biot Savart Law -

dB = \frac{uo * I * dL X 1r}{4\pi r^{2} }

dB = \frac{uo *I * dL * sin\alpha }{4\pi R^{2} }

For the complete loop , integrate along the circumference 2piR.

=> B  =  [(uo * I)/(4πR²)]∫dL

=>  B  =  [(uo * I)/(4πR²)] * 2πR

=>  B = (uo * I)/(2R)

Thus, Magnetic field at centre of loop =  (uo * I)/(2R)

where, uo = 4π * 10^-7   T.m/A

Magnetic field along axis of loop

By integrating z component we can calculate magnetic field on axis of loop .

dBz = \frac{uo * I * dL * R}{4\pi{(z^{2} +R^{2}})*\sqrt{z} ^{2} +R^{2}   }

Integrating along circumference of circle

=>  Bz  =  (uo/4π) * [(2πR²I)/(z²+R²)√(z²+R²)]

Thus, Magnetic field along axis of loop is given by -

Bz  =  (uo/4π) * [(2πR²I)/(z²+R²)√(z²+R²)]

Attachments:
Answered by parthph1357
1

Answer:

Biot Savart Law

Biot Savart Law is an equation that describes the magnetic field created by a current carrying wire and allows us to calculate its strength at various points .

According to Biot Savart Law , the magnetic field produced by infinitesimal length of conductor is given by -

dB = \frac{uo * I * dL X 1r}{4\pi r^{2} }dB=

4πr

2

uo∗I∗dLX1r

where, dL = infinitesimal length of conductor carrying current

1r = unit vector directing from current to field point.

Magnetic field at centre of loop

According to Biot Savart Law -

dB = \frac{uo * I * dL X 1r}{4\pi r^{2} }dB=

4πr

2

uo∗I∗dLX1r

dB = \frac{uo *I * dL * sin\alpha }{4\pi R^{2} }dB=

4πR

2

uo∗I∗dL∗sinα

For the complete loop , integrate along the circumference 2piR.

=> B = [(uo * I)/(4πR²)]∫dL

=> B = [(uo * I)/(4πR²)] * 2πR

=> B = (uo * I)/(2R)

Thus, Magnetic field at centre of loop = (uo * I)/(2R)

where, uo = 4π * 10^-7 T.m/A

Magnetic field along axis of loop

By integrating z component we can calculate magnetic field on axis of loop .

dBz = \frac{uo * I * dL * R}{4\pi{(z^{2} +R^{2}})*\sqrt{z} ^{2} +R^{2} }dBz=

4π(z

2

+R

2

)∗

z

2

+R

2

uo∗I∗dL∗R

Integrating along circumference of circle

=> Bz = (uo/4π) * [(2πR²I)/(z²+R²)√(z²+R²)]

Thus, Magnetic field along axis of loop is given by -

Bz = (uo/4π) * [(2πR²I)/(z²+R²)√(z²+R²)]

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