Question #115733
A long straight wire carries a current of 1.5 A. an electron travels with a speed of 5 x 106 cm/s parallel to the wire 10 cm from it and in the same direction as the current. What force does the magnetic field of the current exert on the moving electron.
1
Expert's answer
2020-05-15T08:42:13-0400

Magnetic field around the long straight wire carrying current is a well-known result, which can be obtained using Bio-Sawart law or Ampere's law: B=μ0I2πRB = \frac{\mu_0 I}{2 \pi R}. The field is circular, and centered around the wire.

Magnetic field acts on the charged particle with Lorentz force: F=qv×B\bold F = q \bold v \times \bold B. Since, in our case the magnetic field is circular in the plane, perpendicular to the wire, and electron is moving along the wire, v\bold v is perpendicular to B\bold B, so the absolute value of the cross product in the Lorentz force is just vBv B. Therefore, F=qvB=qvμ0I2πRF = q v B = \frac{q v \mu_0 I}{2 \pi R}. Substituting given values for I,v,RI, v, R and permeability μ0=4π107TmA\mu_0 = 4 \pi \cdot 10^{-7} \frac{T m}{A}, obtain: F=2.41024NF = 2.4 \cdot 10^{-24} N.


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