Question

An alpha particle (charge +2e) and an electron move in opposite directions from the same point, each with the speed of 2.80×10^5 m/s . Find the total magnetic field these charges produce at point P, which is 8.25 nm from each charge. μ0=4πx10^-7 H/m, 1nm= 10^-9 m.

Answer 1

Answer:

Explanation:

Magnetic field due to moving charge =

$B=\frac{\mu_0}{4\pi} \times \frac{qv}{r^2}$

q is charge moving with velocity v and r is distance from point at which field is calculated .

For alpha particle

$B_1=\frac{\mu_0}{4\pi} \times \frac{2\times 1.6\times10^{-19}\times 2.8\times 10^5}{(8.25\times 10^{-9})^2}$

= 0.1316 x 10⁻³ T

For electron

$B_2=\frac{\mu_0}{4\pi} \times \frac{ 1.6\times10^{-19}\times 2.8\times 10^5}{(8.25\times 10^{-9})^2}$

= .0658 x 10⁻³ T .

Both these magnetic field will be same in direction because direction of equivalent current is same for both the particles .

Hence

Total magnetic field

= B₁ + B₂ = .1974 x 10⁻³

= 1.974 x 10⁻⁴ T .