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  • (a) Depict the magnetic field lines due to a circular current carrying loop showing the direction of field lines. (b) A current I is flowing in a conductor placed along the x-axis as shown in the figure. Find th

(a) Depict the magnetic field lines due to a circular current carrying loop showing the direction of field lines.
(b) A current I is flowing in a conductor placed along the x-axis as shown in the figure. Find the magnitude and direction of the magnetic field due to a small current element \vec{dl}
 lying at the origin at points (i) (0, d, 0) and (ii) (0, 0, d).

 

 

 

Answers (1)

a)
 
This figure shows magnetic field lines due to a circular current-carrying loop. The direction of the magnetic field line is found by using the Right-hand thump rule. At the centre of the circular loop, the magnetic field line is straight and perpendicular to the plane of the coil.
b)
     
The relation between current and magnetic field is given by Biot-Savart's law.
From Biot-Savart's law, the magnetic of the field is
          \left | dB \right |= \frac{\mu _{0}}{4\pi }\: \: \frac{Idl\sin \theta }{r^{2}}
where \theta is the angle between current element i\overrightarrow{dl} and the displacement vector 'r'.
i) (0,d,0)
 which implies point is in y-axis
 Here \overrightarrow{dl}  is in x-axis , so \theta = 90^{\circ}
\sin 90^{\circ}= 1
Therefore the magnitude of the magnetic field is

\frac{\mu _{0}}{4\pi }\: \frac{Idl}{d^{2}}
the direction of the magnetic field is along with positive z-axis dl
The direction is perpendicular to the plane containing dl and v
ii) (0,0,d)
which implies point is in the z-axis
\theta = 90^{\circ}  so, \sin 90^{\circ}= 1
The magnitude of the magnetic field is

\frac{\mu _{0}}{4\pi }\: \frac{Idl}{r^{2}}
The direction of the magnetic field is along negative y-axis
In the direction, i) found by using the Screw rule of the cross product.

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