A 5.30-ìC charge is moving with a speed of 9.30 x 104 m/s parallel to a very long, straight wire. The wire is 6.60 cm from the charge and carries a current of 87.0 A. Find the magnitude of the force on the charge.
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To find the magnitude of the force on the charge, we can use the formula for the magnetic force between a moving charge and a current-carrying wire:
F = (µ₀ * I * q * v) / (2 * π * r)
where:
F is the magnitude of the force
µ₀ is the permeability of free space (4π x 10^-7 T m/A)
I is the current in the wire
q is the charge
v is the velocity of the charge
r is the distance between the charge and the wire
Plugging in the given values:
µ₀ = 4π x 10^-7 T m/A
I = 87.0 A
q = 5.30 x 10^-6 C
v = 9.30 x 10^4 m/s
r = 6.60 cm = 6.60 x 10^-2 m
Now we can calculate the magnitude of the force by substituting these values into the formula:
F = (4π x 10^-7 T m/A * 87.0 A * 5.30 x 10^-6 C * 9.30 x 10^4 m/s) / (2 * π * 6.60 x 10^-2 m)
Simplifying the expression:
F = (4π x 10^-7 T m/A * 87.0 A * 5.30 x 10^-6 C * 9.30 x 10^4 m/s) / (2π * 6.60 x 10^-2 m)
F = (4 * 87.0 * 5.30 x 10^-7 * 9.30 x 10^4) / (2 * 6.60 x 10^-2) T
F = (2.23 x 10^-3) T
Therefore, the magnitude of the force on the charge is approximately 2.23 x 10^-3 Tesla.