4.5.4 Force on a current-carrying conductor (3)
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1.
A rectangular loop of wire has length 0.5 m and width 0.3 m. The wire carries a current of 5A and is placed in a uniform magnetic field of 0.8 T. The magnetic field is perpendicular to the plane of the loop. Calculate the magnitude of the magnetic force acting on the loop. Show your working.
Formula: The magnetic force on a current-carrying loop is given by:
F = N x I x A x sin(θ)
where:
- N = Number of turns in the loop (assumed to be 1 for a single loop)
- I = Current (in Amperes)
- A = Area of the loop (in m2)
- θ = Angle between the magnetic field and the normal to the loop (which is 90° in this case)
Calculations:
N = 1
I = 5 A
A = length x width = 0.5 m x 0.3 m = 0.15 m2
θ = 90°
F = 1 x 5 A x 0.15 m2 x 1 = 0.75 N
Answer: The magnitude of the magnetic force acting on the loop is 0.75 N.
2.
An electron is moving with a velocity of 2.0 x 107 m/s in a magnetic field of 0.5 T. The electron is moving parallel to the magnetic field. What is the magnitude and direction of the force on the electron? (Charge of an electron = -1.60 x 10-19 C)
When the velocity of a charged particle is parallel to the magnetic field, the magnetic force is zero. This is because sin(90°) = 1, and the force is proportional to sinθ. Therefore, F = qvBsinθ = qvBsin(90°) = qvB.
In this case, the velocity (v) is parallel to the magnetic field (B), so θ = 90 degrees and sin(90°) = 1.
Therefore, F = (-1.60 x 10-19 C) * (2.0 x 107 m/s) * (0.5 T)
F = -1.60 x 10-18 N
The magnitude of the force is 1.60 x 10-18 N, and the direction is parallel to the magnetic field (because the charge is negative).
3.
A current of 2A flows through a wire placed in a magnetic field of 0.5 T. The wire is oriented so that the magnetic field is pointing into the page. Calculate the magnitude of the magnetic force acting on a 0.2 m length of the wire. Show your working.
Formula: The magnitude of the magnetic force (F) on a current-carrying conductor in a magnetic field is given by:
F = I x L x B x sin(θ)
where:
- I = Current (in Amperes)
- L = Length of the conductor in the magnetic field (in meters)
- B = Magnetic field strength (in Teslas)
- θ = Angle between the current and the magnetic field
Calculation:
I = 2 A
L = 0.2 m
B = 0.5 T
θ = 90° (since the wire is perpendicular to the magnetic field), sin(90°) = 1
F = 2 A x 0.2 m x 0.5 T x 1 = 0.2 N
Answer: The magnitude of the magnetic force is 0.2 N.