a bar magnet whose radius is 20 cm from its center is used to search for an iron pin of the magnetic lines from around the magnets to attract the iron pin is given as 40m webars.
determine the magnetic flux density produced by the bar magnet?
To determine the magnetic flux density produced by the bar magnet, we need to use the formula:
B = μ0 * (M / (2 * π * r^3))
Where:
B is the magnetic flux density
μ0 is the permeability of free space (constant value of 4π × 10^-7 T·m/A)
M is the magnetic moment of the bar magnet
r is the distance from the center of the magnet to the point where the magnetic flux density is being measured
Given that the magnetic lines from the bar magnet attract an iron pin with a flux of 40 mWb (milli-Webers), we can use this information to calculate the magnetic moment (M) of the bar magnet.
M = Φ / A
Where:
M is the magnetic moment
Φ is the magnetic flux
A is the area through which the magnetic flux passes (in this case, the cross-sectional area of the iron pin)
Now, let's take the given information and calculate the magnetic moment (M):
Φ = 40 mWb = 40 × 10^-3 Wb (converting milli-Webers to Webers)
The radius of the bar magnet is given as 20 cm, so the diameter is 40 cm or 0.4 meters. Assuming the bar magnet is cylindrical in shape, the cross-sectional area (A) of the iron pin can be calculated using the formula:
A = π * r^2
Let's continue our calculation:
A = π * (0.2)^2 (converting the radius to meters)
Now that we have the value of A, we can calculate the magnetic moment (M):
M = 40 × 10^-3 Wb / (π * (0.2)^2)
Now, we can substitute the calculated value of M into the formula for magnetic flux density (B):
B = μ0 * (M / (2 * π * r^3))
Given that r = 0.2 meters, and μ0 is a constant value of 4π × 10^-7 T·m/A, we can calculate the magnetic flux density (B).