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The magnetic induction at the centre of a current carrying circular coil of radius 10cm is 5√5 times the magnetic induction at a point on its axis. The distance of the point from the centre of the coil in cm is
- a)5
- b)10
- c)20
- d)25
Correct answer is option 'C'. Can you explain this answer?
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To find the magnetic induction at the center of a current carrying circular coil, we can use the formula for the magnetic field inside a circular coil:
B = (μ₀ * n * I) / (2 * R)
Where:
B is the magnetic induction (in Tesla)
μ₀ is the permeability of free space (4π * 10^-7 T*m/A)
n is the number of turns per unit length (in m^-1)
I is the current flowing through the coil (in Amperes)
R is the radius of the coil (in meters)
In this case, we are given that the radius of the coil is 10 cm, which is equal to 0.1 meters. We are also given that the magnetic induction at the center of the coil is 5 Tesla.
Let's plug in these values into the formula:
5 = (4π * 10^-7 T*m/A) * n * I / (2 * 0.1 m)
Simplifying the equation:
5 = (2π * 10^-7 T*m/A) * n * I
Now, we need to find the value of n * I. Since we don't have any information about the number of turns per unit length or the current flowing through the coil, we cannot determine the exact value of n * I.
Therefore, without additional information, we cannot determine the magnetic induction at the center of the current carrying circular coil.
B = (μ₀ * n * I) / (2 * R)
Where:
B is the magnetic induction (in Tesla)
μ₀ is the permeability of free space (4π * 10^-7 T*m/A)
n is the number of turns per unit length (in m^-1)
I is the current flowing through the coil (in Amperes)
R is the radius of the coil (in meters)
In this case, we are given that the radius of the coil is 10 cm, which is equal to 0.1 meters. We are also given that the magnetic induction at the center of the coil is 5 Tesla.
Let's plug in these values into the formula:
5 = (4π * 10^-7 T*m/A) * n * I / (2 * 0.1 m)
Simplifying the equation:
5 = (2π * 10^-7 T*m/A) * n * I
Now, we need to find the value of n * I. Since we don't have any information about the number of turns per unit length or the current flowing through the coil, we cannot determine the exact value of n * I.
Therefore, without additional information, we cannot determine the magnetic induction at the center of the current carrying circular coil.
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The magnetic induction at the centre of a current carrying circular coil of radius 10cm is 5√5 times the magnetic induction at a point on its axis. The distance of the point from the centre of the coil in cm isa)5b)10c)20d)25Correct answer is option 'C'. Can you explain this answer?
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