An electron travels at a speed of 5.56×107 m/s along the z-axis. What is the magnetic field at the point (0.00 cm,7.00 cm,7.00 cm) when the electron passes through the origin?Magnitude:
Question
An electron travels at a speed of 5.56×107 m/s along the z-axis. What is the magnetic field at the point (0.00 cm,7.00 cm,7.00 cm) when the electron passes through the origin?Magnitude:
Solution
The magnetic field B created by a moving charge q (like an electron) at a distance r can be calculated using the Biot-Savart law:
B = μ0/4π * (q*v) / r^2
where:
- μ0 is the permeability of free space, which is 4π × 10^-7 T m/A,
- q is the charge of the electron, which is -1.6 × 10^-19 C,
- v is the speed of the electron, which is given as 5.56 × 10^7 m/s,
- r is the distance from the electron to the point where we want to calculate the magnetic field.
The point (0.00 cm,7.00 cm,7.00 cm) is a distance r = sqrt((0.00 cm)^2 + (7.00 cm)^2 + (7.00 cm)^2) = 9.899 cm = 0.099 m away from the origin.
Substituting these values into the Biot-Savart law gives:
B = (4π × 10^-7 T m/A) / 4π * ((-1.6 × 10^-19 C) * (5.56 × 10^7 m/s)) / (0.099 m)^2
Solving this equation will give the magnitude of the magnetic field at the point (0.00 cm,7.00 cm,7.00 cm) when the electron passes through the origin.
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