The magnetic field inside a solenoid is given by:
B=μ0ni,
where:
- B=6.28×10−3T is the magnetic field,
- μ0=4π×10−7T m/A is the permeability of free space,
- n=ℓm is the number of turns per unit length,
- i=5A is the current,
- ℓ=0.5m is the length of the solenoid.
Step 1: Rearranging the Formula
Substituting the given values:
μ0(ℓm)i=B.
Rearranging to find m:
m=μ0iBℓ.
Step 2: Substituting the Values
Substituting the given values:
m=4π×10−7×56.28×10−3×0.5.
Simplifying:
m=12.56×10−76.28×10−3×0.5.
Further simplification:
m=12.56×10−73.14×10−3.
Calculating:
m=500.
Therefore, the value of m is 500.