An electron is moving along positive x-axis. A uniform electric field ...
Let the velocity of the electron is v
Then
If the electric field is E then
Lorentz Force
or, For force to be zero
or, To get the RHS in the direction of , B should be acting in the direction of . As we know that Therefore the direction of the magnetic field must be in the negative z-axis.
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An electron is moving along positive x-axis. A uniform electric field ...
Explanation:
To find the direction of the magnetic field that will result in a net force of zero on the electron, we can use the right-hand rule for the cross product of the electric and magnetic fields. According to this rule, the direction of the magnetic field can be determined by placing the fingers of the right hand in the direction of the electric field and then curling them towards the magnetic field.
Given:
Electric field direction: towards negative y-axis
Electron's motion: along positive x-axis
Step 1: Determine the direction of the electric field
The electric field is given to be towards the negative y-axis. This means that the electric field vector points downwards in the y-axis direction.
Step 2: Determine the direction of the electron's velocity
The electron is moving along the positive x-axis. This means that the velocity vector of the electron points towards the positive x-axis direction.
Step 3: Apply the right-hand rule
To find the direction of the magnetic field, we need to curl the fingers of the right hand from the direction of the electric field (downwards) towards the direction of the electron's velocity (positive x-axis).
Result:
Using the right-hand rule, we find that the magnetic field direction is perpendicular to both the electric field and the velocity of the electron. The resulting magnetic field direction is along the negative z-axis (out of the page). Therefore, the correct answer is option 'B' - Negative z-axis.
An electron is moving along positive x-axis. A uniform electric field ...
Negative zDue to electric field force is in positive y directonfor net force zero on electron force due to magnetic field must be in negative y direction direction of magnetic field is in negative z direction