Question

At what distance x from the center of the coil, on the axis of the coil, is the magnetic field half its value at the center?

Answer 1

The value of x is 2.1 cm from the center of the coil.

Step-by-step explanation:

Radius, R = 2.7 cm

Number of turns, N = 800

The magnetic field at the axis is half of the magnetic field at the center.

`B_(axis)=(B_(center))/(2)\\\\(\mu o)/(4\pi)* \frac{2 \pi I N R^2}{\left (R^2 + x^2 \right )^{(3)/(2)}} = 0.5(\mu o)/(4\pi)*(2\pi N I)/(R)\\\\(R^2)/((R^2 + x^2)^(3)/(2)) = (1)/(2R)\\\\4R^6 = (R^2+x^2)^3\\\\1.6 R^2 = R^2 + x^2\\\\x^2 = 0.6 * 2.7* 2.7 \\\\x = 2.1 cm`