A research team uses a thin rectangular gold foil of thickness to determine the…

PHYSICS · Multi-part · CBSE · Physics · Moving Charges and Magnetism · Moving Charges and Magnetism

Problem

A research team uses a thin rectangular gold foil of thickness

t = 25\,\mu\text{m}

to determine the number density of mobile electrons in gold. The foil is placed so that a uniform magnetic field of magnitude

B = 0.35\,\text{T}

is perpendicular to its surface (

+z

direction). A variable conventional current

I

is sent along the

+x

direction, and the resulting transverse potential difference

V

between the upper and lower edges (

\pm y

) is recorded. The measured data are: Current

I

(A): 0.50, 1.00, 1.50, 2.00 Potential difference

V

(µV): 0.92, 1.86, 2.79, 3.67 (a) Using the data, describe the mathematical relationship you observe between

V

and

I

. Support your description with appropriate reasoning. (b) Express the electron number density

n

in terms of the slope of a

V

-versus-

I

graph, the foil thickness

t

, the magnetic field

B

, and the elementary charge

e

. (c) Determine a numerical value for

n

from the data provided. (d) The thickness measurement has an uncertainty of

\pm5\%

. Discuss how this uncertainty propagates into the calculated value of

n

and indicate whether it represents a systematic or a random error.