A current path shaped as shown in the figure produces a magnetic field at P, the
ID: 3898283 • Letter: A
Question
A current path shaped as shown in the figure produces a magnetic field at P, the center of the arc. If the arc subtends an angle of theta = 40.0degree and the radius of the arc is 0.700 m, what are the magnitude and direction of the field produced at P if the current is 2.00 A? The unit of magnetic flux is named for Wilhelm Weber. A practical-size unit of magnetic field is named for Johann Karl Friedrich Gauss. Along with their individual accomplishments, Weber and Gauss built a telegraph in 1833 that consisted of a battery and switch, at one end of a transmission line 3 km long, operating an electromagnet at the other end. Suppose their transmission line was as diagrammed in the figure below. Two long, parallel wires, each having a mass per unit length of 31.5 g/m, are supported in a horizontal plane by strings l = 6.30 cm long. When both wires carry the same current I, the wires repel each other so that the angle between the supporting strings is theta = 15.8degree.Explanation / Answer
since the current in straight path do not contribute to filed at P
B = int (dB) = (uI/4pie) * int (ds*r)/r^2
= (uI/4pie * r^2) * S
theta = 40* pie/180 = (pie/4.5) rad
S = r * theta = 0.7 * pie/4.5
hence
B = {u(2.0)(0.7)pie/4.5}/4pie * (0.7)^2
= 4pie*10^-7 * 2/ 28*0.7 = 199.46*10^-9 T = 199.46 nT