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=
`(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 =
`(B*2\pi r)/(u_(0) )`

B, 2π and
`u_(0)` are all constants, thus

`(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

`(I_(1) )/(r_(1) )`=
`(I_(2) )/(r_(2) )`

`r_(1)`=1cm and
`r_(2)`=11cm

`(1_(1) )/(1)`=
`(I_(2) )/(11)`

thus
`I_(2)`=11*
`I_(1)`

which means the second current is 11 times the first current