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Magnetic Force on Current-Carrying Wire.

Created by @nathanedwards
 at November 2nd 2023, 4:21:06 pm.
AP_Physics_2-Questions
#physics
#magnetic-force
#current-carrying-wire

Question:

A wire of length 2 meters carries a current of 3 Amperes. The wire is placed in a uniform magnetic field of 0.5 Tesla, perpendicular to the direction of the wire. Calculate the magnetic force experienced by the wire.

Solution:

The magnetic force experienced by a current-carrying wire in a magnetic field can be calculated using the formula:

F=I⋅L⋅B⋅sin⁡(θ) F = I \cdot L \cdot B \cdot \sin(\theta)

where: F = Magnetic force on the wire I = Current flowing through the wire L = Length of the wire B = Magnetic field strength θ = Angle between the direction of the current and the magnetic field

In this case, the wire is perpendicular to the magnetic field, so the angle θ is 90 degrees. The length of the wire is given as 2 meters, the current as 3 Amperes, and the magnetic field as 0.5 Tesla.

Using the formula, we can calculate the magnetic force:

F=3 A⋅2 m⋅0.5 T⋅sin⁡(90∘) F = 3 \text{ A} \cdot 2 \text{ m} \cdot 0.5 \text{ T} \cdot \sin(90^\circ)

Since sin(90°) = 1, the equation simplifies to:

F=3 A⋅2 m⋅0.5 T⋅1 F = 3 \text{ A} \cdot 2 \text{ m} \cdot 0.5 \text{ T} \cdot 1

Simplifying further:

F=3 A⋅1 T F = 3 \text{ A} \cdot 1 \text{ T}

The units for magnetic force are Newtons.

Hence, the magnetic force experienced by the wire is 3 Newtons.

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