Question

If you push a coil of wire through a magnetic field where the field direction is perpendicular to the plane of the coil and the direction of the coil’s velocity, a voltage is induced in the coil with a magnitude

V=NBlv

where N is the number of turns in the coil, B is the magnitude of the magnetic field, l is the length of the side of the coil that is perpendicular to the velocity direction and lowercase v is the velocity of the coil. If you make a plot of Voltage vs velocity, the slope of that graph will be NBl. Add calculations to the cell block below to find the predicted value of the slope, along with its uncertainty. You may use either the functional or calculus method to find the uncertainty. Make sure that your answer has units and the appropriate number of digits.

I'm looking for the equation for the functional or calculus method to find the uncertainty.

I1 import numpy as n # Calculate the slope of a Voltage vs velocity graph along with the uncertainty # in the slope N 100 # The number of turns is exactly known and doesn't have an uncertainty B 0.032 # Teslas Bunc 0.003 # Teslas 1 7.4 # cm lunc 0.2 #cm # Fill in the calculation for the slope and the uncertainty in the slope slope N (B/100) (1/100) slopeunc # Warning: the lengths 1 and lunc are given in cm, make sure you convert to the correct # units! # Change the print statement below to output the correct number of digits for # both the slope and its uncertainty # Add the correct units for slope to the print statement print( 'slope %. 3f \u00B1 %. 3f' % (slope, slopeu nc)) NameError Traceback (most recent call last) kipython-input-2-f6505866c17a> in <module>(O) 21 # Add the correct units for slope to the print statement > 23 print( 'slope %. 3f \u00B1 %.3f' % (slope, slopeunc )) NameError: name slope' is not defined SEARCH STACK OVERFLOW

Answer 1

The program has been implemented in Python 3 and code is commented for easy understanding:

# Calculate the slope of a Voltage vs velocity graph along with the uncertainty in the slope

N = 100 # The number of turns is exactly known and doesn't have an uncertainty

B = 0.032 # Teslas

Bunc = 0.003 # Teslas

Bunc_percent=Bunc*100/B #percentage error in B

l = 7.4 # cm

lunc = 0.2 #cm

lunc_percent=lunc*100/l #percentage error in l

total_unc=Bunc_percent+lunc_percent #total percentage error

unc=(total_unc*B*l)/100 #uncertainity in B and l

# Fill in the calculation for the slope and the uncertainty in the slope

slope= N * B * (l/100)

slopeunc= N * (unc/100)

# Warning: the lengths l and lunc are given in cm, make sure you convert to the correct units!

# Change the print statement below to output the correct nun-der of digits for :

# both the slope and its uncertainty

# Add the correct units for slope to the print statement.

print( 'slope = %.3f ± %.3f' % (slope, slopeunc))

Output:

slope = 0.237 ± 0.029

Python 3.6.1 (default, Dec 2015, 13:05:11) [GCC 4.8.2] on linux slope0.237 t 0.029