A current I = 16 A is directed along the positive x-axis and perpendicular to a magnetic field. A magnetic force per unit length of 0.15 N/m acts on the conductor in the negative y-direction. Calculate the magnitude and direction of the magnetic field in the region through which the current passes.
When the current I and mgnetic field B are perpendicular,
F = B I L
In your case, force per unit length F/L = 0.15 N/m; therefore
B = (0.15 N/m)/16 A = 9.4*10^-3 Tesla
The direction of the field is the z direction. As to whether it is up or down, use the right-hand rule to get the direction of I x B, and make sure it is in the -y dorection
To find the magnitude and direction of the magnetic field, we'll use the formula for the magnetic force on a current-carrying conductor:
F = BIL
Where:
F is the magnetic force on the conductor per unit length
B is the magnetic field strength
I is the current in the conductor
L is the length of the conductor
In this case, the magnetic force per unit length is given as 0.15 N/m, the current is 16 A, and the length can be taken as 1 meter (since it doesn't affect the calculation of the magnetic field magnitude).
Plugging in the given values into the formula, we have:
0.15 N/m = B * 16 A * 1 m
Now, we can solve for B:
B = 0.15 N/m / (16 A * 1 m)
B = 0.009375 T
Therefore, the magnitude of the magnetic field is 0.009375 Tesla (T).
To determine the direction of the magnetic field, we apply the right-hand rule. When the index finger points in the direction of the current (positive x-axis), and the thumb points in the direction of the magnetic force (negative y-axis), the middle finger will point in the direction of the magnetic field.
In this case, the magnetic field is directed in the positive z-direction (out of the page or towards you).
So, the magnitude of the magnetic field is 0.009375 T and it is directed in the positive z-direction.
To calculate the magnitude and direction of the magnetic field, we can use the formula for the magnetic force experienced by a current-carrying wire:
F = I * L * B * sin(θ)
Where:
F is the magnetic force
I is the current in the wire
L is the length of the wire
B is the magnetic field
θ is the angle between the wire and the magnetic field
In this case, the magnetic force per unit length is given as 0.15 N/m. Since the current I = 16 A, we know that the length L = 1 m (because the magnetic force is given per unit length).
From the formula, we can rearrange it to solve for the magnetic field B:
B = F / (I * L * sin(θ))
Given that F = 0.15 N/m, I = 16 A, L = 1 m, and sin(θ) = 1 (since the magnetic force acts in the negative y-direction perpendicular to the current), we can substitute these values:
B = 0.15 N/m / (16 A * 1 m * 1)
B = 0.15 N/m / 16 A
Calculating this, we find:
B ≈ 0.0094 T
So, the magnitude of the magnetic field is approximately 0.0094 Tesla.
The direction of the magnetic field can be determined using the right-hand rule. If the current is directed along the positive x-axis and the magnetic force is directed in the negative y-direction, then the direction of the magnetic field would be along the positive z-axis (upwards).