Question

An investigator places a sample 1.0 cm from a wire carrying a large current; the strength of the magnetic field has a particular value at this point. Later, she must move the sample to a 11.0 cm distance, but she would like to keep the field the same. Part A) By what factor must she increase the current?

Answer 1

Answer: she will have to increase the factor of current by 11

Explanation: The mathematical relationship between the strength of the magnetic field (B) created by a current carrying conductor with current (I) is given by the Bio-Savart law given below

B=$\frac{u_{0}I }{2\pi r}$

B=strength of magnetic field

I = current on conductor

r = distance on any point of the conductor from it center

u$_{0}$ = permeability of magnetic field in space

from the question, the investigator is trying to keep a constant magnetic field meaning B has a fixed value such as the constants in the formulae, the only variables here are current (I) and distance (r). We can get this a mathematical function.

by cross multipying, we have

B* 2πr=$u_{0}$I

by dividing through to make I subject of formulae, we have that

I = $\frac{B*2\pi r}{u_{0} }$

B, 2π and $u_{0}$ are all constants, thus

$\frac{B*2\pi r}{u_{0} }$ = k(constant)

thus we have that

I =kr (current is proportional to distance assuming magnetic field strength and other parameters are constant)

thus we have that

$\frac{I_{1} }{r_{1} }$=$\frac{I_{2} }{r_{2} }$

$r_{1}$=1cm and $r_{2}$=11cm

$\frac{1_{1} }{1}$=$\frac{I_{2} }{11}$

thus $I_{2}$=11* $I_{1}$

which means the second current is 11 times the first current