A 0.0150-m wire oriented horizontally between the poles of an electromagnet carries a direct current of 9.5 A. The angle between the direction of the current and that of the magnetic field is 25.0° as shown. If the magnetic field strength is 0.845 T, what is the magnitude and direction of the magnetic force on the wire between the poles?
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To find the magnitude and direction of the magnetic force on the wire between the poles, we can use the formula for the magnetic force on a current-carrying wire:
F = I * L * B * sin(θ)
where:
F is the magnetic force,
I is the current,
L is the length of the wire,
B is the magnetic field strength, and
θ is the angle between the direction of the current and the magnetic field.
Given:
I = 9.5 A (current)
L = 0.0150 m (length of the wire)
B = 0.845 T (magnetic field strength)
θ = 25.0° (angle)
Let's calculate the magnetic force step by step:
1. Convert the angle from degrees to radians:
θ_radians = θ * (π / 180) = 25.0° * (π / 180) = 0.4363 radians
2. Plug the values into the formula:
F = I * L * B * sin(θ_radians) = 9.5 A * 0.0150 m * 0.845 T * sin(0.4363 radians)
3. Calculate sin(0.4363 radians):
sin(0.4363 radians) ≈ 0.423
4. Calculate the magnetic force:
F = 9.5 A * 0.0150 m * 0.845 T * 0.423 ≈ 0.0574 N
Therefore, the magnitude of the magnetic force on the wire between the poles is approximately 0.0574 N.
To determine the direction of the magnetic force, we can use the right-hand rule. If you point your right thumb in the direction of the current (from positive to negative), and your fingers in the direction of the magnetic field, your palm will face the direction of the magnetic force.
To find the magnitude and direction of the magnetic force on the wire, we can use the equation for the magnetic force on a current-carrying wire:
F = BILsinθ
where:
F is the magnetic 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 current direction and the magnetic field direction.
Now, let's solve the problem step by step:
Step 1: Identify the values given in the problem:
- Magnetic field strength (B) = 0.845 T
- Current (I) = 9.5 A
- Length of the wire (L) = 0.0150 m
- Angle between current direction and magnetic field direction (θ) = 25.0°
Step 2: Convert the angle from degrees to radians:
Since the trigonometric functions in most calculators use radians, it's easier to convert the angle to radians:
θ (in radians) = θ (in degrees) × π/180
θ (in radians) = 25.0° × π/180 = 0.4363 radians
Step 3: Use the formula to calculate the magnetic force:
F = BILsinθ
F = (0.845 T)(9.5 A)(0.0150 m)sin(0.4363 radians)
F = 0.0113 N
Therefore, the magnitude of the magnetic force on the wire between the poles is 0.0113 N.
Step 4: Determine the direction of the magnetic force:
The direction of the magnetic force can be determined using the right-hand rule: If you point your right thumb in the direction of the current, and curl your fingers towards the magnetic field direction, your extended palm will give you the direction of the force.
In this case, the current is flowing from left to right (horizontal wire), and the magnetic field is directed into the page (as indicated by the cross symbol). Using the right-hand rule, the magnetic force will be directed downwards towards the bottom of the page.
Therefore, the direction of the magnetic force on the wire between the poles is downwards.