Question

A long, straight wire carries a current of 5.20 A. An electron is traveling in the vicinity of the wire.At the instant when the electron is 4.70 cm from the wire and traveling with a speed of 5.80×10^4 m/s directly toward the wire, what is the magnitude of the force that the magnetic field of the current exerts on the electron?

Answer 1

The magnitic field due to an infinite long current carrying conductor is $B= \frac{\mu _{0}i}{2\pi r}$

From Biot-Savart law $\bar{dB}= \frac{\mu _{0}i\bar{dl}x\hat{r}}{2\pi r}$

Therefore     $B= \frac{4\pi x10^{-7}xi}{2\pi r}$

                    B= 2.21x10^-5T

Now the force on moving charge is F=QVB

           Force on electron F= 1.6x10^-19x5.8x10⁴ x2.21x10^-5

                                      F = 20.51x10^-20N

It is perpedicular to the conductor.