Question

Find magnetic field at the center of current carrying circular wire . Draw magnetic field lines also.

Answer 1

The magnitude of magnetic field at the centre is the sum of magnitude of magnetic fields at the two points of the circular wire.

Hope this helps you...:)

Answer 2

Consider a circular coil of radius a and carrying current I in the direction shown in Figure. Suppose the loop lies in the plane of paper. It is desired to find the magnetic field at the centre O of the coil. Suppose the entire circular coil is divided into a large number of current elements, each of length dl. According to Biot-Savart law, the magnetic field at the centre O of the coil due to current element I is given by;

where is the position vector of point O from the current element. The magnitude of at the centre O is

The direction of is perpendicular to the plane of the coil and is directed inwards. Since each current element contributes to the magnetic field in the same direction, the total magnetic field B at the center O can be found by integrating the above equation around the loop i.e.


For each current element, angle between and is 90°. Also distance of each current element from the center O is a. Therefore

Now, dl = Total length of the coil
= 2 a

If the coil has n turns, each carrying current in the same direction, then contributions of all the turns are added up, then
B =