How Do You Calculate Proton Velocity Components in a Magnetic Field?

[frankfjf]

Homework Statement

A proton moves through a uniform magnetic field given by B = (10i - 20j +30k)mT. At time t1, the proton has a velocity given by v = vxi + vyj + (2.0km/s)k and the magnetic force on the proton is F = (4.0 x 10^-17N)i + (2.0 x 10^-17N)k. At that instant, what are (a) vx and (b) vy?

Homework Equations

F = qv x B

The Attempt at a Solution

After taking the cross product I get an equation that looks like:

4 x 10^-17Ni + 2 x 10^-17Nj = e(.03vy + 40)i + (20 - .03vx)j - (.02vx - .01vy)k

It's at this point that I blank out. The Student Solutions Manual says that the next step is to equate corresponding components, but what do they mean by this? Set vy to zero then solve for vx and vice versa?

 

[frankfjf]

Nevermind! I figured it out.

 

[Proof.Beh]

we have F=|q|v*B then according to determinant (matrix.JPG) derive that
q(-40-3vy)i-q(20-3vx)j+q(10vy+20vx)k=F then we get

q(20-3vx)=0 --> vx=20/3
q(10vy+20vx)k=2*10^{-17} --> vy

Has it any problem?

Thanks.
Mr Beh

 

[bilal232lagcc]

What is the solution to this problem ... I am stuck at the same step as you were ? Please Help

 

[asteriatic]

Hello,

Thank you for your question. I would approach this problem by first identifying the known and unknown variables. In this case, we know the magnetic field (B), velocity (v), and magnetic force (F) of the proton, and we are trying to find the components of velocity (vx and vy) at time t1.

Next, I would use the equation F = qv x B to solve for the unknown velocities. This equation represents the cross product of the velocity and magnetic field vectors, which results in the magnetic force vector. By equating the components of the force vector (Fx and Fy) to the corresponding components of the cross product (qv x B), we can solve for vx and vy.

Therefore, the next step would be to set the x-component of the force (Fx) equal to the x-component of the cross product (qv x B). Similarly, the y-component of the force (Fy) would be set equal to the y-component of the cross product. This will result in two equations with two unknowns (vx and vy), which can be solved using algebraic methods.

I hope this helps. Let me know if you have any further questions.