A 550-turn solenoid is 15 cm long. The current in it is 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A current downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?
To calculate the force on the wire, we can use the formula for the magnetic force experienced by a current-carrying wire in a magnetic field. The formula is given by:
F = B * I * L * sinθ
Where:
- F is the force on the wire,
- B is the magnetic field strength,
- I is the current in the wire,
- L is the length of the wire, and
- θ is the angle between the direction of the current and the magnetic field.
Let's break down the steps to solve the problem:
Step 1: Find the magnetic field strength
The magnetic field inside a solenoid is given by the formula:
B = μ₀ * N * I
Where:
- μ₀ is the permeability of free space (4π * 10^-7 T·m/A),
- N is the number of turns in the solenoid, and
- I is the current in the solenoid.
Given:
- N (number of turns) = 550 turns
- I (current in the solenoid) = 33 A
Substituting the given values into the formula, we can calculate the magnetic field strength inside the solenoid.
B = (4π * 10^-7) * 550 * 33
Step 2: Calculate the angle between the current and magnetic field
Since the wire cuts through the center of the solenoid along a diameter, the angle θ between the current and the magnetic field is 90 degrees (perpendicular).
θ = 90 degrees
Step 3: Calculate the force on the wire
Now we have all the values required to calculate the force using the formula:
F = B * I * L * sinθ
Given:
- L (length of the wire) = 3.0 cm = 0.03 m
- I (current in the wire) = 22 A
- θ (angle between the current and magnetic field) = 90 degrees
Substituting the given values into the formula, we can calculate the force on the wire.
F = B * I * L * sinθ
Finally, calculate the force by substituting the calculated magnetic field strength (B) and the given values of current (I), wire length (L), and angle (θ) into the formula.
magnetic filed is = mu*numberturns*current all that is given for the solenoid.
now that you know magnetic field B in the solenoid, then
force on the wire: currentinwire*length*B*sinTheta