At what distance from a long straight wire carrying a current of 10 A is the magnetic field equal to the earth's magnetic field of 5 ｘ 10⁻⁵ T? (Answer: 0.04 m) 



Given:

Current =  I =  10 A

Magnetic Field = B = 5 ｘ 10⁻⁵ T

Permeability of free space = µ₀ = 4 ã„« ï½˜ 10⁻⁷ H m⁻¹

To Find:

Radial Distance from the wire = r = ?


Solution:

Using Ampere's Law

B = `\frac {µ₀ I}{2ã„«r}`

or

r = `\frac {µ₀ I}{2ã„«B}`

by putting the corresponding values

r = `\frac { 4ã„« ｘ 10⁻⁷ H m⁻¹ ｘ10 A}{2ã„« ｘ 5 ｘ 10⁻⁵ T}`

r = `\frac { 40ã„« ｘ 10⁻⁷ H m⁻¹ A}{10ㄫｘ 10⁻⁵ T}`

r = 40ｘ 10⁻³  m

r = 4 ï½˜ 10⁻² m

or 

 r = 0.04 m ------------------ Ans.



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⭐ Henry 'H' is the unit of measurement for Inductance:

1 H = Wb A⁻¹ =  V s A⁻¹ = kg m² s⁻² A⁻²   [Wb= Weber, A=Ampere, V=Volt]



⭐ Weber 'Wb' is the unit of measurement for Magnetic Flux:

1 Wb =  V s = kg m² s⁻² A⁻¹   = H A




⭐ Tesla 'T' is the unit of measurement for Magnetic Field:

1 T =  N m⁻¹ A⁻¹ = kg m s⁻² A⁻¹   


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