At a particular instant a proton is at the origin, moving with velocity < 7 ? 10

Question

At a particular instant a proton is at the origin, moving with velocity < 7 ? 104, -3 ? 104, -6 ? 104 > m/s. At this instant:

hint: The electric field is just the Coulomb electric field of a point charge. To calculate the magnetic field, use the Biot-Savart law for a single particle.

At a particular instant a proton is at the origin, moving with velocity m/s. At this instant: (a) What is the electric field at location m, due to the proton? B = T hint: The electric field is just the Coulomb electric field of a point charge. To calculate the magnetic field, use the Biot-Savart law for a single particle. E = N/C (b) What is the magnetic field at the same location due to the proton?

Explanation / Answer

(a)
All you need to find the electric field using the formula is to find the square of the distance of the point from the origin.
=> r^2 = (4x10^-3)^2 + (4x10^-3)^2 + (2x10^-3)^2 = 36x10^-6 m^2
=> E = (8.99x10^9 * 1.6x10^-19) / (36x10^-6) N/C = 4 x 10^-5 N/C.
This is the magnitude of the electric field and its direction is towards the r (vector).

(b)
Magnitude of magnetic field formula should be
(?o/4?) Q * l (velocity vector x unit vector r) l / r^2
= (?o/4?) Q * l (velocity vector x vector r) l / r^3

= 10^-7 * 1.6x10^-19 * l [(7, -3, -6) x (4, 4, 2)] l x10 / (36x10^-6)^3 Tesla

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