Answer:
Explanation:
magnetic field due to a current carrying infinite wire
B = μ₀ / 4π x (2i / r )
i is current , r is perpendicular distance of point from the wire
Let at a point d distance away fro wire 1 , field is zero , let the current in wire 1 and 2 be 4i and i .
between them at any point field will be in opposite direction .
magnetic field due to wire 1
B₁ = μ₀ / 4π x (2i / r )
= 10⁻⁷ x 2 x 4i / d
magnetic field due to wire 2
B₂ = μ₀ / 4π x (2i / r )
= 10⁻⁷ x 2 x i / ( 1 - d )
for zero field
B₁ =B₂
10⁻⁷ x 2 x 4i / d = 10⁻⁷ x 2 x i / ( 1 - d )
4 / d = 1 /( 1 - d )
4 ( 1 - d ) = d
4 -4d = d
4 = 5d
d = 4 / 5
= .8 m
The perpendicular distance from the wire to a place of zero magnetic field is 0.8 m.
When a conductor carries current it produces magnetic field was first discovered by Hans Christian Oersted (1777 - 1851).
The magnetic field produced due in this case has the following features:
Let the magnetic field due to a current carrying infinite wire be B
B = μ₀ / 4π x (2 i / r )
where
i is current
r is perpendicular distance
current in wire 1 = 4 i
current in wire 2 = i
The distance between wire 1 and wire 2 such that at this distance the magnetic field B is zero hence the fields are equal. that is B 1 = B 2
where B 1 is magnetic field for wire 1 and B 2 is the magnetic field for wire 2.
Since they carry current in same direction distance between them are
r 1 + r 2 = 1 m
r 1 = 1 - r 2
distance for wire 1 = r
distance for wire 2 = 1 - r
B 1 = B 2
μ₀ / 4π x (2 (4*i)/ r ) = μ₀ / 4π x (2 i / 1 - r )
( 4 * i ) / r = i / ( 1 - r)
4 / r = 1 / ( 1 - r )
4 ( 1 - r ) = r
4 - 4 r = r
4 = 5 r
r = 4/5 = 0.8 m
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