The strength of the magnetic field at the center of a circular loop carrying current is directly proportional to:Options:A) The radius of the loopB) The square of the radius of the loopC) The current passing through the loopD) The resistance of the loop
Question
The strength of the magnetic field at the center of a circular loop carrying current is directly proportional to:Options:A) The radius of the loopB) The square of the radius of the loopC) The current passing through the loopD) The resistance of the loop
Solution
The strength of the magnetic field at the center of a circular loop carrying current is directly proportional to the current passing through the loop. So, the correct answer is C) The current passing through the loop.
Here's why:
The formula for the magnetic field (B) at the center of a circular loop of radius (r) carrying a current (I) is given by Ampere's Law as:
B = μ0I/(2π*r)
Where:
- B is the magnetic field
- μ0 is the permeability of free space
- I is the current
- r is the radius of the loop
From this equation, we can see that the magnetic field (B) is directly proportional to the current (I) and inversely proportional to the radius (r). Therefore, the strength of the magnetic field increases with increasing current and decreases with increasing radius.
The resistance of the loop is not a factor in this equation, so it does not directly affect the strength of the magnetic field.
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