Albert's laboratory is filled with a constant uniform magnetic field pointing straight up. Albert throws some charges into this magnetic field. He throws the charges in different directions, and observes the resulting magnetic forces on them. Given the sign of each charge and the direction of its velocity, determine the direction of the magnetic force (if any) acting on the charge.

(a) Positive charge moving south
(b) Negative chatge moving west
(c) Negative charge not moving at all

a) West direction

b) South direction

c) Force is zero

Explanation:

- The direction of the magnetic force acting on a charged particle moving in a cross-magnetic field can be given by Fleming's Left hand rule.

- The left hand rule says:

           Direction of middle finger : Direction of charge particle velocity

           Direction of Index finger : Direction of magnetic field

           Direction of Thumb : Direction of magnetic force.

a) So when a + charge moves south. The left hand middle finger points south. While index finger points upward or out of the page. Then the thumb would point in West direction.

b) So when a - charge moves west it also means a positive charge is moving to East. The left hand middle finger points East. While index finger points upward or out of the page. Then the thumb would point in South direction.

c) So when a - charge does not move at all. Then the cross product of 0 and magnetic field is also zero. Hence, Force is zero.

step-by-step explanation:

we are given

we have to simplify it

firstly, we will factor it

now, we can cancel like terms

now, we can combine it

so, we get