Two parallel, straight wires that are very long are separated by a distance of 0.065
m and carry currents of I1 =15 A and I2 =7.0A. Find the magnitude and direction of
the force that the magnetic field of wire 1 applies to a 1.5-m section of wire 2 when
the currents have opposite directions.
To find the magnitude and direction of the force between the two wires, we can use the formula for the magnetic force between two parallel wires:
F = (mu0 * I1 * I2 * L) / (2 * pi * d)
where:
- F is the magnitude of the force between the wires
- mu0 is the permeability of free space, which is approximately equal to 4 * pi * 10^-7 Tm/A
- I1 and I2 are the currents in the two wires
- L is the length of the section of wire 2
- d is the distance between the wires
Plugging in the given values:
I1 = 15 A,
I2 = 7.0 A,
L = 1.5 m,
d = 0.065 m
mu0 = 4 * pi * 10^-7 Tm/A
F = (4 * pi * 10^-7 Tm/A * 15 A * 7.0 A * 1.5 m) / (2 * pi * 0.065 m)
Simplifying the equation, we can cancel out pi, the units of meters, and the units of Amperes:
F = (4 * 15 * 7.0 * 1.5) / (2 * 0.065) N
Evaluating this expression gives:
F = 294 N
The magnitude of the force between the wires is 294 N.
To determine the direction of the force, we can use the right-hand rule. Place your right hand so that your thumb points in the direction of the current flowing through wire 2. Then, curl your fingers toward wire 1. The direction your palm faces indicates the direction of the force between the wires.
In this case, the force will be directed into the plane of the paper (or computer screen).
So, the magnitude of the force is 294 N and the direction is into the paper.
To find the magnitude and direction of the force between the two parallel wires, you can use the formula for the magnetic force between two current-carrying wires.
The formula for the magnetic force between two parallel wires is given by:
F = μ₀ * (I1 * I2 * L) / (2 * π * d)
Where:
F is the magnitude of the force,
μ₀ is the permeability of free space (constant value),
I1 and I2 are the currents flowing in the two wires,
L is the length of the wire segment, and
d is the distance between the wires.
First, let's calculate the magnitude of the force using the given values:
F = (4π * 10^-7 T*m/A) * (15 A * 7.0 A * 1.5 m) / (2 * π * 0.065 m)
Simplifying, we have:
F = (4π * 10^-7 T*m/A) * (157.5 A² * m) / (2 * π * 0.065 m)
F = 12.09 * 10^-6 N
So the magnitude of the force is approximately 12.09 μN.
Now, let's determine the direction of the force using the right-hand rule. Place the right hand on wire 2 with your fingers pointing in the direction of the current in wire 2. Then, curl your fingers towards wire 1. The direction your thumb points gives you the direction of the force.
In this case, since the currents in wire 1 and wire 2 are opposite, the force direction will be towards wire 1.
Therefore, the force between the two wires has a magnitude of approximately 12.09 μN and acts towards wire 1.