## Sunday, September 4, 2016

### Magnetic Field Strength due to Current Problems and Solutions

We know that the magnetic field at the center of circular part due to straight line part of the conductor carrying conductor is zero. It is simply because the point is on the conductor itself.

We also know how to measure the field due to a circular part of the conductor and it is the total field itself. It is measured as shown in the above diagram.

We can also the find the direction of the magnetic field using the cork screw rule. Simply if the curled fingers indicates the direction of the current, the thumb indicates the direction of the magnetic field and that is inwards as shown.

Problem and solution

We need to find the magnetic field at the center of the circular arc part of the diagram where it is also has the current carrying conductor in straight shape.

The upper part of the straight conductor is at a distance equal to the radius of the arc and hence at the center of arc there will be magnetic field due to that straight conductor. According to the cark screw rule or thumb rule, the direction of the magnetic field is inwards.

The arc part also generates some magnetic induction and it can be measured as shown in the diagram below basing on the previous law. Its direction is outward.

The third part of the straight conductor will also generates some magnetic field induction and its direction is also outward.

To find the total magnetic field due to all of them, we shall add all the magnetic fields as shown in the diagram and with proper sign.

Problem and solution

We can solve one more problem basing on the same concept. We would like to measure the magnetic field at the center of the coil as shown below. We need to measure the field due to each part and we shall add all of them with proper sign to get the total magnetic field at the center.

Problem and solution

We need to find the magnetic field at the center of the coil that has infinite ladders as shown below. We just need to apply the formula that we have learned in the previous case and need to add all of them to get the total magnetic field as shown below.

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