At a point high in the Earth’s atmosphere, He 2+ ions in a concentration of 2.8 X 1012/m3 are moving due north at a speed of 2.0 X 105 m/s. Also, a 7.0 X 1011/m3 concentration of O2 ions is moving due south at a speed of 7.2 X 106 m/s. Determine the magnitude and direction of the net current passing through unit area (A/m2).
To determine the magnitude and direction of the net current passing through unit area (A/m2), we need to use the formula for current density (J):
J = q * v * n
Where:
- J is the current density (A/m2)
- q is the charge of the ion (Coulombs)
- v is the velocity of the ion (m/s)
- n is the concentration of the ions (m-3)
The magnitude of the net current density passing through unit area can be found by subtracting the current densities of the two ion species:
J_net = J_He2+ - J_O2
Now, we'll calculate the current densities for each ion species:
For He 2+ ions:
q_He2+ = 2 * e (charge of an electron)
v_He2+ = 2.0 X 105 m/s
n_He2+ = 2.8 X 1012/m3
J_He2+ = q_He2+ * v_He2+ * n_He2+
For O2 ions:
q_O2 = 2 * e
v_O2 = -7.2 X 106 m/s (negative since it's moving south)
n_O2 = 7.0 X 1011/m3
J_O2 = q_O2 * v_O2 * n_O2
Now, we substitute the values and calculate the current densities:
q_He2+ = 2 * 1.6 x 10^-19 C = 3.2 x 10^-19 C
v_He2+ = 2.0 X 105 m/s
n_He2+ = 2.8 x 10^12/m3
J_He2+ = (3.2 x 10^-19 C) * (2.0 X 105 m/s) * (2.8 x 10^12/m3)
q_O2 = 2 * 1.6 x 10^-19 C = 3.2 x 10^-19 C
v_O2 = -7.2 X 106 m/s
n_O2 = 7.0 x 10^11/m3
J_O2 = (3.2 x 10^-19 C) * (-7.2 X 106 m/s) * (7.0 x 10^11/m3)
Now, we can calculate the net current density passing through unit area:
J_net = J_He2+ - J_O2
Finally, we can find the magnitude and direction:
Magnitude = |J_net|
Direction = Direction of J_net (either north or south)
By following these calculations, you can determine the magnitude and direction of the net current passing through unit area (A/m2).