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 7.0 cm distance, but she would like to keep the field the same. By what factor must she increase the current?

Answer 1

she must increase the current by factor of 7

Step-by-step explanation:

The magnetic field produced by a steady current flowing in a very long straight wire encircles the wire.In order to solve the question, we use this formula,

B= μo I/(2πr)

where,

'μo' represents permeability of free space i.e 4π*10-7 N/A2

B=magnetic field

I= current

r=radius

->When r= 1cm=> 0.01m

B1 = μo
`I_{1`/(2π x 0.01)

->when r=7cm =>0.07m

B2 = μo
`I_(2)`/(2π x 0.07)

Now equating both of the magnetic fields, we have

B1= B2

μo
`I_{1`/(2π x 0.01)= μo
`I_(2)`/(2π x 0.07)

`I_{1`/
`I_(2)`= 0.01/0.07

`I_{1`/
`I_(2)`= 1/ 7

Therefore, she must increase the current by factor of 7