Question

While measuring the distance of the magnetic sensor in your phone from the center of the magnet (or coil) you decided to include uncertainties from two places. One is the uncertainty in locating the center of the magnet (or coil) and you estimated it as 0.25 cm. The other is the uncertainty in locating the position of the sensor in the phone and you estimated it as 0.45 cm. What is the uncertainty in the distance measurement when calculated using quadrature method

Answer 1

Answer:

the uncertainty in the distance measurement is 0.5148

Explanation:

Given the data in the question;

uncertainty in locating the center of the magnet is estimated to be 0.25 cm,

uncertainty in locating the position of the sensor in the phone is estimated to be 0.45 cm,

Using quadrature method, uncertainty in the distance measurement = ?

We know that;

Using  quadrature method, Combined Uncertainty calculated by;

U$_c$ = √( U₁² + U₂² + ........... )

where U₁ is uncertainty in first measurement and U₂ is uncertainty in second measurement, et cetera.

now we substitute;

U$_c$ = √( U₁² + U₂² )

U$_c$ = √( (0.25)² + (0.45)² )

U$_c$ = √( 0.0625 + 0.2025 )

U$_c$ = √( 0.265 )

U$_c$ = 0.5148

Therefore, the uncertainty in the distance measurement is 0.5148