A proton moves through a region of space where there is a magnetic field B = (0.45i + 0 38j) T and an electric field E = ( 3.0 i – 4.2 j ) x 10^3 V/m. At a given instant, the proton’s velocity is V = ( 6.0 i + 3.0 j - 5.0 K ) x10^3 m/s . Determine the components of the total force on the proton.

Question

A proton moves through a region of space where there is a magnetic field  B = (0.45i + 0 38j) T and an electric field E = ( 3.0 i – 4.2 j ) x 10^3 V/m. At a given instant, the  proton’s velocity is V = ( 6.0 i + 3.0 j - 5.0 K ) x10^3 m/s . Determine the components of the total  force on the proton.

jamesj · Answer

There is of course an electric force and a magnetic force (Lorentz force) on the proton.  Do you know how to calculate each?

anonymous · Answer

yes..i know its about electric force and magnetic force...but, i dont know how to calculate...

jamesj · Answer

The electric force is straightforward: F = Eq where E is the electric field.

The magnetic force requires you to use the Lorentz force
$$ F_{magnetic} = q(v \times B) $$
where B is the magnetic field vector and v is the velocity vector.

anonymous · Answer

ok...but how about the alphabet in that equation?

jamesj · Answer

alphabet?

anonymous · Answer

such as B = (0.45i + 0 38j) T.. alphabet i and j...

jamesj · Answer

This is vector notation.  i, j and k are the unit vectors in the x, y and z directions respectively.

anonymous · Answer

@JamesJ ..so,each vector notation are calculate separately,right? but,how about 'K'? the answer maybe 0,right?

jamesj · Answer

that K should be k, the unit vector in the z direction.

anonymous · Answer

but only velocity vector that only have unit vector k...so,total force for k component is zero,right?

jamesj · Answer

No.  You have to calculate the vector cross product with B, which is all in the i and j directions, and those will definitely interact with the k component of the velocity vector.