Q. Two identical circular wires P and Q each of radius R and carrying current I are kept in perpendicular planes such that they have a common centre as shown in the figure. Find the magnitude and direction of the net magnetic field at the common centre the two coils.
Answers
Given:
Two identical circular wires P and Q each of radius R and carrying current I are kept in perpendicular planes such that they have a common centre as shown in the figure.
To find:
Find the magnitude and direction of the net magnetic field at the common centre the two coils.
Solution:
From given, we have,
Two identical circular wires P and Q each of radius R and carrying current I are kept in perpendicular planes such that they have a common centre.
Consider the attached figure while going through the following steps.
B{R} = √[B{P}² + B{Q}²]
where,
B{Q} is directed horizontally and B{P} is directed vertically.
So, we have,
B{P} = B{Q} = μ₀I/2R
B = √2B{P} = √2B{R}
⇒B = √2 (μ₀I/2R)
∴ B = μ₀I/√2R
Hence the required resultant magnetic field.
Direction of magnetic field is given by,
tan θ = B{P}/B{Q}
as, B{P} = B{Q}, so we get,
tan θ = B{P}/B{P}
∴ tan θ = 1
⇒ θ = tan^{-1} 1
∴ θ = 45°
Therefore, the magnitude and direction of the resultant magnetic field is μ₀I/√2R and 45° with either of the fields.
