How to Calculate Current Needed for a Solenoid to Produce a Specific Magnetic Field

A solenoid with a length of 34.0 cm and a diameter of 1.25 cm is required to produce a magnetic field of 4.60 mT at its center. How much current should the solenoid carry?

To determine the amount of current the solenoid should carry to produce a specific magnetic field, we can use the formula B = μnI. By calculating the number of loops per unit length and plugging in the given values, we can solve for the current. In this case, the solenoid should carry a current of 20.8 A.

To determine the amount of current the solenoid should carry, we can use the formula B = μnI, where B is the magnetic field, μ is the permeability of free space, n is the number of loops per unit length, and I is the current. We are given the length and diameter of the solenoid, so we can use these values to find the number of loops per unit length. From there, we can plug in the values for B and μ and solve for I.

First, we calculate the number of turns per unit length (n):
n = 2000 / (1000 × 0.1) = 20 turns/cm

Next, we convert the length of the solenoid to meters:
length = 34.0 cm = 0.34 m

Now we can calculate the current (I):
B = μnI ⇒ I = B / (μn) = 4.60 mT / (4π×10-7 Tm/A × 20 turns/m × 0.34 m) = 20.8 A

Therefore, the solenoid should carry a current of 20.8 A to produce the desired magnetic field.