Physics study guide question? Lost. What do I do first? Using Biot-Savart Law.?

Question

Segment of wire with current I=.5m where the radius of circular arc is R=2cm. How would I use the Biot-Savart Law to develop an equation describing the magnetic field at the center of the square.


(There is a small graph showing the +x-axis and +yaxis. The current I is moving from the positive x direction towards the origin. and there is 1/4 of a circle that goes from the +x to +y axis. The radius of this is drawn from the center of it to the origin.)

Answer 1

The Biot-Savart law for a circular current loop is

B = µ0*I/(2*R); This is derived from the basic differential form of the law:

dB = (µ0/4π)*I*dl x rˆ/r^2, where rˆ is the unit vector in the direction of I. For a circular uniform current, the cross product produces a vector for B along the axis of the circle, deifined by the right-hand rule for cross products. dl becoms ds, the element of arc along the circle:

dB = µ0*I/4π * ds/r^2,

When integrated for a circular loop of radius R, ds becomes R*dø. The integral from 0 to 2π is then 2πR. The law then reduces to

µ0*I/4π • 2πR/R^2 = µ0*I/4π * 2π/R = µ0*I/(2*R)

Answer 2

Not at all.