Magnetic Force physics detailed explanation please including

Magnetic Force, physics. detailed explanation please including any relevant formulas

Negative charge moves -Y, B points Y, what is the direction of force applied on the charge? Positive charge moves -X, B points -Y, what is the direction of force applied on the charge? Negative charge moves -Y, B points -Z, what is the direction of force applied on the charge?

Solution

For an electric charge of q moving with velocity V in presence of magnetic field B, the force is given as charge multiplied by the cross product of velocity and magnetic field.

That is, F = qV x B

Now, clearly whether the charge is negative or positive will influence the direction of the cross product.

We will use these to solve the given problems:

Part A.) Here the velocity is along -Y axis and B points +Y axis, hence the cross product of the two will result into zero. Therefore no force acts on the charge.

Part B.) Here a positive charge moves along -X axis and magnetic field is along -Y axis, hence the cross product will point along +z axis.

Therefore the direction of the force acting on the charge would be along +Z axis.

Part C.) Here the charge is travelling along the -Y axis and field is along -Z axis, however, the charge in consideration is negative, hence the direction of the force will be opposite of the cross product of V and B.

Cross product of V and B would point towards +x axis.

Therefore the direction of the force would be along - X axis.