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Two mutually perpendicular conductors carrying currents I1 and I2 lie in one plane. Locus of the point at which the magnetic induction is zero, is a
- a)Circle with centre as the point of intersection of the conductor.
- b)Parabola with vertex as the point of intersection of the conductors
- c)Straight line passing through the point of intersection of the conductors
- d)Rectangular hyperbola
Correct answer is option 'C'. Can you explain this answer?
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Two mutually perpendicular conductors carrying currents I1and I2lie in...
Magnetic field in X-Y plane at position (x,y) due to both wires must be zero
current carrying wire with current i1 is taken along X axis
now the magnetic field at the given point is
B1= μ0i1/2πy
now at the same point the magnetic field due to other wire placed along Y axis is given by,
B2= μ0i2/2πx
now we have to make the magnitude of magnetic field due to both wires same
so, B1=B2
μ0i1/2πy= μ0i2/2πx
now by solving above we have,
y=(i1/i2)x
so it’s a straight line with slope i1/i2 and passing from origin
current carrying wire with current i1 is taken along X axis
now the magnetic field at the given point is
B1= μ0i1/2πy
now at the same point the magnetic field due to other wire placed along Y axis is given by,
B2= μ0i2/2πx
now we have to make the magnitude of magnetic field due to both wires same
so, B1=B2
μ0i1/2πy= μ0i2/2πx
now by solving above we have,
y=(i1/i2)x
so it’s a straight line with slope i1/i2 and passing from origin
Most Upvoted Answer
Two mutually perpendicular conductors carrying currents I1and I2lie in...
To determine the locus of the point at which the magnetic induction is zero, we need to consider the magnetic fields produced by the two currents and find the point where the fields cancel out.
1. Magnetic Field due to I1:
The magnetic field produced at a point P due to a current carrying conductor can be given by the Biot-Savart law. For a straight conductor, the magnetic field at a point P located at a distance r from the conductor is given by:
B1 = (μ0 * I1) / (2πr)
where μ0 is the permeability of free space, I1 is the current in the conductor, and r is the distance from the conductor.
2. Magnetic Field due to I2:
Similarly, the magnetic field produced at point P due to the second conductor carrying current I2 can be given by:
B2 = (μ0 * I2) / (2πr)
3. Magnetic Field at Point P:
The total magnetic field at point P due to both conductors is the vector sum of the fields produced by I1 and I2. Since the conductors are mutually perpendicular, the magnetic fields are also perpendicular.
The resultant magnetic field at point P can be found using the Pythagorean theorem:
B = √(B1^2 + B2^2)
4. Magnetic Induction is Zero:
To find the locus of the point where the magnetic induction is zero, we need to find the point where the total magnetic field B is zero. This occurs when B1 and B2 are equal in magnitude but opposite in direction.
This condition can be expressed as:
B1 = -B2
Substituting the expressions for B1 and B2, we get:
(μ0 * I1) / (2πr) = -(μ0 * I2) / (2πr)
Simplifying, we find:
I1 = -I2
This equation represents a straight line passing through the point of intersection of the conductors. Hence, the correct answer is option 'C' - a straight line passing through the point of intersection of the conductors.
1. Magnetic Field due to I1:
The magnetic field produced at a point P due to a current carrying conductor can be given by the Biot-Savart law. For a straight conductor, the magnetic field at a point P located at a distance r from the conductor is given by:
B1 = (μ0 * I1) / (2πr)
where μ0 is the permeability of free space, I1 is the current in the conductor, and r is the distance from the conductor.
2. Magnetic Field due to I2:
Similarly, the magnetic field produced at point P due to the second conductor carrying current I2 can be given by:
B2 = (μ0 * I2) / (2πr)
3. Magnetic Field at Point P:
The total magnetic field at point P due to both conductors is the vector sum of the fields produced by I1 and I2. Since the conductors are mutually perpendicular, the magnetic fields are also perpendicular.
The resultant magnetic field at point P can be found using the Pythagorean theorem:
B = √(B1^2 + B2^2)
4. Magnetic Induction is Zero:
To find the locus of the point where the magnetic induction is zero, we need to find the point where the total magnetic field B is zero. This occurs when B1 and B2 are equal in magnitude but opposite in direction.
This condition can be expressed as:
B1 = -B2
Substituting the expressions for B1 and B2, we get:
(μ0 * I1) / (2πr) = -(μ0 * I2) / (2πr)
Simplifying, we find:
I1 = -I2
This equation represents a straight line passing through the point of intersection of the conductors. Hence, the correct answer is option 'C' - a straight line passing through the point of intersection of the conductors.
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Two mutually perpendicular conductors carrying currents I1and I2lie in one plane. Locus of the point at which the magnetic induction is zero, is aa)Circle with centre as the point of intersection of the conductor.b)Parabola with vertex as the point of intersection of the conductorsc)Straight line passing through the point of intersection of the conductorsd)Rectangular hyperbolaCorrect answer is option 'C'. Can you explain this answer?
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Two mutually perpendicular conductors carrying currents I1and I2lie in one plane. Locus of the point at which the magnetic induction is zero, is aa)Circle with centre as the point of intersection of the conductor.b)Parabola with vertex as the point of intersection of the conductorsc)Straight line passing through the point of intersection of the conductorsd)Rectangular hyperbolaCorrect answer is option 'C'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Two mutually perpendicular conductors carrying currents I1and I2lie in one plane. Locus of the point at which the magnetic induction is zero, is aa)Circle with centre as the point of intersection of the conductor.b)Parabola with vertex as the point of intersection of the conductorsc)Straight line passing through the point of intersection of the conductorsd)Rectangular hyperbolaCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two mutually perpendicular conductors carrying currents I1and I2lie in one plane. Locus of the point at which the magnetic induction is zero, is aa)Circle with centre as the point of intersection of the conductor.b)Parabola with vertex as the point of intersection of the conductorsc)Straight line passing through the point of intersection of the conductorsd)Rectangular hyperbolaCorrect answer is option 'C'. Can you explain this answer?.
Two mutually perpendicular conductors carrying currents I1and I2lie in one plane. Locus of the point at which the magnetic induction is zero, is aa)Circle with centre as the point of intersection of the conductor.b)Parabola with vertex as the point of intersection of the conductorsc)Straight line passing through the point of intersection of the conductorsd)Rectangular hyperbolaCorrect answer is option 'C'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Two mutually perpendicular conductors carrying currents I1and I2lie in one plane. Locus of the point at which the magnetic induction is zero, is aa)Circle with centre as the point of intersection of the conductor.b)Parabola with vertex as the point of intersection of the conductorsc)Straight line passing through the point of intersection of the conductorsd)Rectangular hyperbolaCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two mutually perpendicular conductors carrying currents I1and I2lie in one plane. Locus of the point at which the magnetic induction is zero, is aa)Circle with centre as the point of intersection of the conductor.b)Parabola with vertex as the point of intersection of the conductorsc)Straight line passing through the point of intersection of the conductorsd)Rectangular hyperbolaCorrect answer is option 'C'. Can you explain this answer?.
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Two mutually perpendicular conductors carrying currents I1and I2lie in one plane. Locus of the point at which the magnetic induction is zero, is aa)Circle with centre as the point of intersection of the conductor.b)Parabola with vertex as the point of intersection of the conductorsc)Straight line passing through the point of intersection of the conductorsd)Rectangular hyperbolaCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Two mutually perpendicular conductors carrying currents I1and I2lie in one plane. Locus of the point at which the magnetic induction is zero, is aa)Circle with centre as the point of intersection of the conductor.b)Parabola with vertex as the point of intersection of the conductorsc)Straight line passing through the point of intersection of the conductorsd)Rectangular hyperbolaCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Two mutually perpendicular conductors carrying currents I1and I2lie in one plane. Locus of the point at which the magnetic induction is zero, is aa)Circle with centre as the point of intersection of the conductor.b)Parabola with vertex as the point of intersection of the conductorsc)Straight line passing through the point of intersection of the conductorsd)Rectangular hyperbolaCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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