A -6.00 µC charge is moving with a speed of 6.60 104 m/s parallel to a very long, straight wire. The wire is 5.00 cm from the charge and carries a current of 73.0 A in a direction opposite to that of the moving charge. Find the magnitude and direction of the force on the charge.
The force is q V B and is perpendicular to both the wire and the B field, which makes it radial inward. (A negative charge moving opposite to the current direction is attracted to the wire).
For B, use Ampere's law of a straight wire.
B = u * I /(2 pi R)
where u is the permeability of free space, which you will have to look up..
R = 0.05 m
It still says this is not correct. I got 1.156e-4
I get the same number, in units of Newtons.
To find the magnitude and direction of the force on the charge, you can use the formula for the magnetic force experienced by a moving charged particle:
F = |q| * |v| * |B| * sin(θ)
Where:
F is the magnitude of the force (in Newtons)
q is the charge of the particle (in Coulombs)
v is the velocity vector of the particle (in meters per second)
B is the magnetic field vector (in Tesla)
θ is the angle between the velocity vector and the magnetic field vector
First, let's calculate the magnetic field created by the current-carrying wire at the position of the charge. We can use Ampere's Law:
B = μ₀ * (I / (2πd))
Where:
B is the magnetic field (in Tesla)
μ₀ is the permeability of free space (4π × 10^-7 T*m/A)
I is the current flowing through the wire (in Amperes)
d is the distance between the wire and the charge (in meters)
Substituting the given values:
I = 73.0 A,
d = 5.00 cm = 0.05 m,
μ₀ = 4π × 10^-7 T*m/A,
B = (4π × 10^-7 T*m/A) * (73.0 A / (2π * 0.05 m))
Simplifying this expression, you can calculate the value of B.
Next, we need to determine the angle between the velocity vector of the charge and the magnetic field vector. As the problem states, the charge is moving in a direction parallel to the wire. In this case, the angle θ between the velocity vector and the magnetic field vector is 0° (or 180° in the opposite direction).
Finally, substitute all the values into the formula for the magnetic force mentioned at the beginning:
F = |q| * |v| * |B| * sin(θ)
Substituting the given values:
q = -6.00 × 10^-6 C,
v = 6.60 × 10^4 m/s,
B = calculated value,
θ = 0° (or 180°),
The result will give you the magnitude of the force. To determine the direction, you need to consider the fact that the charge is negative, thus the force vector will be in the opposite direction of the velocity vector of the charge.