Calculating the Magnetic Field Due to a Current — Question 7

Question 7

Current reversal separates a wire signal from a fixed background field

At a sensor a known distance r from a long wire, the signed tangential field is +18.0 microtesla for current +I and -6.00 microtesla for current -I. A constant background contributes along the same sensor axis. Current reversal preserves its magnitude. Use vacuum permeability $\mu_0\simeq4\pi\times10^{-7}\,\mathrm{T\,m/A}$ where numerical values are needed.

1. Find the wire contribution, background contribution and I for r=.0300 m.

2. If the sensor is moved to 2r with the background unchanged, predict both reversed readings.

Question 7 - Solution

Current reversal separates a wire signal from a fixed background field

(a) Method and calculation

$$B_+=B_0+B_w,\quad B_-=B_0-B_w\Rightarrow B_w=(18-(-6))/2=12.0\,\mu\mathrm T.$$$$B_0=6.00\,\mu\mathrm T,\quad I=\frac{2\pi rB_w}{\mu_0}=\boxed{1.80\,\mathrm A}.$$

(b) Interpretation and further calculation

$$B_w(2r)=B_w(r)/2=6.00\,\mu\mathrm T.$$$$\boxed{B_+(2r)=12.0\,\mu\mathrm T,\quad B_-(2r)=0}.$$

Physical check

A zero reading after reversal need not mean that the wire produces no field; here the wire field cancels the background.