A +6.00 µC charge is moving with a speed of 7.00 x 10^4 m/s parallel to a very long, straight wire. The wire is 5.00 cm from the charge and carries a current of 63.0 A in a direction opposite to that of the moving charge. Find the magnitude and direction of the force on the charge.
___________ mN
B = (4pi x 10^-7)/ 2piR
F = q0 v B sin theta
F = (0.000006)(70000)(0.000001257)(63.0)(1)/ 0.3142
F = 0.000033255 / 0.3142
F = 1.0584 x 10^-4 N
F = 1.0584 x 10^-1 mN
_X_ perpendicular to the wire and directed away from it
___ perpendicular to the wire and directed towards it
___ parallel to the current
___ anti-parallel to the current
___ perpendicular to the plane containing both the wire and the charge
Yes, I cheated and used my two right hands and the right hand rules.
Your response confuses me. Please clarify.
You are correct. I did the direction with the right hand rules (thumb in direction of + current). My direction is the same as yours.
Thanks!
Did you see my response to your comment on my two earlier questions?
My 8:19pm and 8:21 post
Hmm, I see you're feeling a bit charged up about this question! Let's break it down and electrify your knowledge.
To find the magnitude and direction of the force on the charge, we need to use the formulas you've provided. Don't worry, we won't get too wired!
First, let's find the magnitude of the magnetic field (B) at the location of the charge. Using the formula B = (4π × 10^-7) × (63.0 A) / (2π × 0.05 m), and doing some quick calculations, we get B = 0.001257 T.
Now, let's find the angle between the velocity of the charge and the magnetic field. Since they are parallel, the angle is 0 degrees. So we can simplify the equation.
Next, we use the formula for the force on a charged particle moving through a magnetic field, F = q0 × v × B × sin(theta). But since sin(0) is 0, we can simplify even further.
Finally, plug in the values: F = (6.00 × 10^-6 C) × (7.00 × 10^4 m/s) × (0.001257 T) × (sin 0°), which simplifies to F = 0. What a shocking revelation!
So, the magnitude of the force on the charge is 0 N. As for the direction, since there is no force acting on the charge, we can say it is non-existent. Like the invisible force of my jokes!
I hope that gives you a jolt of knowledge about the magnitude and direction of the force on the charge. If you need any more electrifying explanations, don't hesitate to ask!
To find the magnitude and direction of the force on the charge, we can use the equation for the magnetic force on a moving charge:
F = q0 * v * B * sin(theta)
Where:
F is the force on the charge,
q0 is the charge of the moving charge (+6.00 µC),
v is the velocity of the charge (7.00 x 10^4 m/s),
B is the magnetic field strength,
and theta is the angle between the velocity of the charge and the magnetic field.
First, let's find the value of B. According to Ampere's Law, the magnetic field produced by a current-carrying wire at a distance r from the wire is given by:
B = (μ0 * I) / (2 * pi * R)
Where:
μ0 is the permeability of free space (4π x 10^-7 Tm/A),
I is the current in the wire (63.0 A),
and R is the distance between the charge and the wire (5.00 cm = 0.05 m).
Plugging in the values:
B = (4π x 10^-7 Tm/A * 63.0 A) / (2π * 0.05 m)
B = (0.000001257 Tm/A * 63.0 A) / 0.3142
B = 0.000079, approximately.
Now, we need to find the angle between the velocity of the charge and the magnetic field, theta. In this case, the two are parallel since they are both moving in the same direction.
Therefore, sin(theta) = sin(0) = 0.
Plugging in the values into the equation for the force:
F = (0.000006 C)(70000 m/s)(0.000079 T)(0) / 0.3142
F = 0
The magnitude of the force on the charge is 0 N.
Since the force is 0 N, we don't have a well-defined direction.