Question

An equilateral triangle is made by uniform wires AB, BC, CA. A current I enter at A and leaves from the midpoint of BC. If the lengths of each side of the triangle are L, the magnetic field B at the centroid O of the triangle is

Answer 1

In this equation, we will see the basics of magnetic field, current in any loop. This will help us to find the answer to the question. Further, we will study the basics of magnetic field and also, we will learn the two rules to find the direction of magnetic field for our better understanding.

Complete answer:
As we know that, equal current flows in part 1 and 2 of the given triangular loop as shown in the figure below:

Now, we are given that the both parts of the triangular loop are symmetric about the point O. So, the magnetic field at O due to both parts is equal and opposite of each other. So, magnitudes of magnetic field at O due to part 1 cancel out the magnitude of magnetic field at O due to part 2.
Therefore, the net magnetic field B at point O is zero.

Additional information:
A magnetic field B can be defined as a vector field that tells the magnetic influence on moving electric charges, electric currents, and magnetized materials. Also, we should know that a charge that is moving in a magnetic field experiences a force that is perpendicular to its town velocity and to the magnetic field.
Fleming's left-hand rule is used to find the direction of magnetic force acting in electric motors. We know that an electric current and magnetic field exist in an electric motor, and these lead to the force that creates the motion. So, the left hand rule is used here which gives the direction of magnetic force acting in the electric motor.

Fleming's right-hand rule is used to find the direction of induced current in an electric generator. As we know that in an electric generator, the motion and magnetic field exist and these lead to the production of an electric current in the generator.

So, the right hand rule is used here to find the direction of induced current in an electric generator.

Note:
Do remember the rules because both the rules tell the different fields. Further, we need to notice the direction of the magnetic field i.e., whether the field is inward or outward. All the three fingers should be placed perpendicular to each other.