What is the Correct Way to Calculate Magnetic Force on an Electron or Proton?

[SHOORY]

<Moderator's note: Moved from a technical forum and thus no template.>

So there was this question
An electron that has velocity (2*10^6 i +3*10^6 j)m/s
moves through the uniform magnetic field (0.03 i - 0.15 j) T
(a) Find the force on the electron due to the magnetic field. (b) Repeat your calculation for a proton having the same velocity.
so I used this equation
F=q(vx By + vy Bx)
By is negative so I put negative and the answer was -3.364*10^-14
but the correct answer is 6.2*10^-14 and we gut it when we use By positive
Why do we have to use it positive although it is in the negative direction?

 

[BvU]

so I used this equation
F=q(vx By + vy Bx)

check that + sign...

 

[SHOORY]

check that + sign...

i am sure of it its from my school book

 

[berkeman]

F=q(vx By + vy Bx)

Are you familiar with the vector form of the Lorentz Force equation? That would make the signs, etc., easier to see.

 

[Chandra Prayaga]

That + sign is wrong, irrespective of what book it is from.

 

[SHOORY]

That + sign is wrong, irrespective of what book it is from.

why is it wrong
do you know what it means
it means the total force

 

[Chandra Prayaga]

why is it wrong
do you know what it means
it means the total force

The total force is: $\vec F~=~q(\vec {v}~X~\vec B)$
The cross product of $\vec v$ and $\vec B$ means that the force components are:
F_x = q(v_yB_z - v_zB_y)
F_y = q(v_zB_x - v_xB_z)
F_z = q(v_xB_y - v_yB_x)
The negative signs do not mean that you are subtracting forces. They are part of the rule for calculating the cross product of two vectors. With the negative signs present, it gives the total force.

 

[SHOORY]

The total force is: $\vec F~=~q(\vec {v}~X~\vec B)$
The cross product of $\vec v$ and $\vec B$ means that the force components are:
F_x = q(v_yB_z - v_zB_y)
F_y = q(v_zB_x - v_xB_z)
F_z = q(v_xB_y - v_yB_x)
The negative signs do not mean that you are subtracting forces. They are part of the rule for calculating the cross product of two vectors. With the negative signs present, it gives the total force.

Oh my god i was wrong all along thank you