Current I flows right-to-left along a wire that has been bent into a semicircula

Question

Current I flows right-to-left along a wire that has been bent into a semicircular arc of radius R:

(a) What is the contribution to the magnetic field at the center of the semicircle due to the straight segments of wire? (This should not require a difficult calculation.)

(b) What direction does the magnetic field at the center of the semicircle point?

(c) Set up and evaluate an integral to determine the magnetic field at the center of the semicircle.

Please show all your work and relevant formulae, also any crucial information to understanding the approach. Thank you this helps me to fully understand this topic. Thank you.

Explanation / Answer

a)

As the point is along the axis of the straight wire the magnetic field due to straight wire is 0

b)

Using Right Hand Thumb Rule, for the specified direction of the current, the magnetic field is directed into the plane

c)

magnetic field due to a full circular current element, B = u*I/(2*R)

where I =current

u = permeability of free space

R = radius

Now, for the semicircular portion of the wire: the magnetic field must be half of it.

So, B = u*I/(4*R) <------answer

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