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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. Part A) By what factor must she increase the current?

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To solve this problem we will apply the concepts related to the magnetic field, which is defined as the relationship between the current and the perimeter of the circumference multiplied by the free space constant, mathematically that is,

[tex]B = \frac{\mu_0}{2\pi}\frac{I}{R}[/tex]

Here,

[tex]\mu_0[/tex] = Permeability at free space

For our first case,

[tex]R = 1cm = 0.01m[/tex]

[tex]B_1 = \frac{\mu_0}{2\pi}\frac{I_1}{0.01}[/tex]

For the second case,

[tex]R = 7cm = 0.07m[/tex]

[tex]B_2 = \frac{\mu_0}{2\pi}\frac{I_2}{0.07}[/tex]

Equation both magnetic field,

[tex]B_1 = B_2[/tex]

[tex]\frac{\mu_0}{2\pi}\frac{I_1}{0.01}=\frac{\mu_0}{2\pi}\frac{I_2}{0.07}[/tex]

[tex]\frac{I_1}{I_2} = \frac{0.01}{0.07}[/tex]

[tex]\frac{I_1}{I_2} = \frac{1}{7}[/tex]

She must increase the current by a factor of 7.

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