A proton, at rest in some region of space where there is an electric and magneti

Question

A proton, at rest in some region of space where there is an electric and magnetic field, experiences a net electromagnetic force of 8.0 x 10-13 N pointing in the positive-x direction. If the same proton then moves with a speed of 1.5 x 106 m/s in the positive-y direction, the net electromagnetic force on it decreases in magnitude to 7.5 x 10-13 N, still pointing in the positive-x direction. Find the magnitude and direction of both the electric field and the magnetic field in which this proton is moving.

Explanation / Answer

When at rest, the only force acting on the proton is the electric force

So, Eq = 8*10^-13 N

where E = eclectric field

q = 1.6*10^-19 C

So, E = 8*10^-13/(1.6*10^-19)

So, E = 5*10^6 N/C directed in positive x -direction

Now, when moving in +y direction,

Magnetic force acting on it, Fm = q*v*B

Now for decrease in net force, the magnetic force Fm must be directed in -ve x direction

So, for this to happen, magnetic field B must be directed in - z axis

So, -Fm + Eq = 7.5*10^-13

So, -qvB + 8*10^-13 = 7.5*10^-13

So, -1.6*10^-19*1.5*10^6*B + 8*10^-13 = 7.5*10^-13

So, B = 0.21 T

So, Electric field = 5*10^6 N/C directed in +x direction <------answer

Magnetic field = 0.21 T directed in -z direction <-------answer

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