A horizontal, straight wire carrying 12 A current from east to west is in the earth's magnetic field B. At this place, B is parallel to the surface of the earth, points north and its magnitude is 0.04mT. Determine the Magnetic Force on 1 m length of wire. If mass of this length of wire is 50g, calculate the value of current in the wire so that its weight is balanced by the magnetic force
To determine the magnetic force on a straight wire, you can use the formula:
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
θ is the angle between the direction of the current and the magnetic field
In this case, the wire is carrying a current from east to west, and the magnetic field is pointing north, which is perpendicular to the current flow. Since the angle between the current and magnetic field is 90 degrees, sin(90) is equal to 1.
Now, let's calculate the magnetic force on 1 meter length of the wire:
F = 12 A * 1 m * (0.04 mT) * sin(90)
= 0.48 mN
So, the magnetic force on 1 meter length of the wire is 0.48 mN.
To balance the weight of the wire with the magnetic force, we need to equate them. The weight of the wire can be calculated using the formula:
Weight = mass * g
where:
Weight is the force due to gravity
mass is the mass of the wire
g is the acceleration due to gravity (approximately 9.8 m/s^2)
Given that the mass of the wire is 50g:
Weight = 50g * 9.8 m/s^2
= 0.05 kg * 9.8 m/s^2
= 0.49 N
So, we need to find the current that produces a magnetic force equal to 0.49 N.
Setting the magnetic force equal to the weight, we have:
0.48 mN = I * 1 m * (0.04 mT) * sin(90)
Simplifying this equation, we find:
I = 0.49 N / (1 m * 0.04 mT)
= 0.49 N / (0.04 N/A)
= 12.25 A
Therefore, the value of the current in the wire should be approximately 12.25 A to balance the weight of the wire with the magnetic force.