What Determines the Magnetic Field Direction in a Square Current Loop?

[aab19902]

Homework Statement

Four electric currents, equal in magnitude are arranged at the corners of a square as shown in the figure.

[URL]https://s1.lite.msu.edu/enc/67/e803dcaee3e6ac1f07ecaa6e11a858c03f3cec0d55e5f69c7b6812a56efcefd2bec6dcdf49316634dcd828e6638a241c37cd7050f1e6c26ba36058828003ed63a62e225561265ad8020044d0aa9e083825ab692fb01f84a9.gif[/URL]

Two currents go into the page, and two are pointing out of the page. Point a is at the center of the square, and points b and c are in the middle of two of the sides. What is the direction of the magnetic field at points a,b, and c?

2. The attempt at a solution
I am clueless really. If I had to guess I would say a is zero. b and c point north.

 

[anathema]

Thank you for your question. I would like to provide you with a more detailed explanation of the direction of the magnetic field at points a, b, and c.

Firstly, it is important to note that the direction of the magnetic field is determined by the right-hand rule. This means that if you point your thumb in the direction of the current, the direction of your fingers will indicate the direction of the magnetic field.

Now, let's consider point a. Since there are four equal currents arranged at the corners of a square, the magnetic field at point a will be zero. This is because the magnetic fields from each current will cancel each other out due to their equal magnitude and opposite direction.

Moving on to point b, we can see that the current at the top left corner is pointing out of the page, while the current at the bottom right corner is pointing into the page. Using the right-hand rule, we can determine that the magnetic field at point b will be directed towards the left side of the square.

Similarly, at point c, the current at the top right corner is pointing out of the page, while the current at the bottom left corner is pointing into the page. Applying the right-hand rule, we can conclude that the magnetic field at point c will be directed towards the right side of the square.

I hope this helps to clarify the direction of the magnetic field at points a, b, and c. If you have any further questions, please do not hesitate to ask. Thank you for your interest in science.