Complete question:
A wire 2.80 m in length carries a current of 5.60 A in a region where a uniform magnetic field has a magnitude of 0.300 T. Calculate the magnitude of the magnetic force on the wire assuming the following angles between the magnetic field and the current.
a) 60 ⁰
b) 90 ⁰
c) 120 ⁰
Answer:
(a) When the angle, θ = 60 ⁰, force = 4.07 N
(b) When the angle, θ = 90 ⁰, force = 4.7 N
(c) When the angle, θ = 120 ⁰, force = 4.07 N
Explanation:
Given;
length of the wire, L = 2.8 m
current carried by the wire, I = 5.6 A
magnitude of the magnetic force, F = 0.3 T
The magnitude of the magnetic force is calculated as follows;
![F = BIl \ sin(\theta)](https://tex.z-dn.net/?f=F%20%3D%20BIl%20%5C%20sin%28%5Ctheta%29)
(a) When the angle, θ = 60 ⁰
![F = BIl \ sin(\theta)\\\\F = 0.3 \times 5.6 \times 2.8 \times sin(60)\\\\F = 4.07 \ N](https://tex.z-dn.net/?f=F%20%3D%20BIl%20%5C%20sin%28%5Ctheta%29%5C%5C%5C%5CF%20%3D%200.3%20%5Ctimes%205.6%20%5Ctimes%202.8%20%5Ctimes%20sin%2860%29%5C%5C%5C%5CF%20%3D%204.07%20%5C%20N)
(b) When the angle, θ = 90 ⁰
![F = BIl \ sin(\theta)\\\\F = 0.3 \times 5.6 \times 2.8 \times sin(90)\\\\F = 4.7 \ N](https://tex.z-dn.net/?f=F%20%3D%20BIl%20%5C%20sin%28%5Ctheta%29%5C%5C%5C%5CF%20%3D%200.3%20%5Ctimes%205.6%20%5Ctimes%202.8%20%5Ctimes%20sin%2890%29%5C%5C%5C%5CF%20%3D%204.7%20%5C%20N)
(c) When the angle, θ = 120 ⁰
![F = BIl \ sin(\theta)\\\\F = 0.3 \times 5.6 \times 2.8 \times sin(120)\\\\F = 4.07 \ N](https://tex.z-dn.net/?f=F%20%3D%20BIl%20%5C%20sin%28%5Ctheta%29%5C%5C%5C%5CF%20%3D%200.3%20%5Ctimes%205.6%20%5Ctimes%202.8%20%5Ctimes%20sin%28120%29%5C%5C%5C%5CF%20%3D%204.07%20%5C%20N)