Magnetic field at center of a 90° circular arc bend

[frozen7]

iv)The magnetic field, B at the center of a circular current loop of radius r carrying current I, is given by the expression . If one of the long straight wires is bent 90o in a circular arc of radius r (refer to Figure B1). What is the magnetic field at the center of the arc P?

Can anyone help me? Help needed.

 

[Päällikkö]

Please show what you've tried.

Use the Biot-Savart law.

 

[frozen7]

What i know is for the arc section, the magnetic field should be (miu)I / 2r and for the straight wire is (miu)I / 2(pie)r. I don't know how to start this question. Should I just sum up both magnetic field?

 

[Päällikkö]

Using the superposition principle, yes you may add them together. The $$\frac{\mu I}{2r}$$ seems to be the magnetic field generated by a whole circle. Thus the field generated by the arc in the picture is $$\frac{1}{4}\frac{\mu I}{2r}$$.

EDIT: Replied the same minute .