# A particle moves through an electric field as shown in the figure. What is the direction of the magnetic field needed to ensure that the particle experiences zero net force?

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A particle moves through an electric field as shown in the figure. What is the direction of the magnetic field needed to ensure that the particle experiences zero net force?

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Step 1

The particle will experience zero net force when the magnetic force and the electric force will cancel each other. For this the magnetic force and the electric force should have equal magnitude and should be opposite to each other.

The equation for the electric field is given by

Step 2

The direction of the magnetic force is given by right hand rule. According to the right hand rule, if the index finger of the right hand points in the direction of the velocity vector, the middle finger in the direction of magnetic field, then thumb will point in the direction of the magnetic force. Pointing thumb to the left of the figure (opposite to the direction of electric  field) and index figure in the upward direction makes the magnetic field to point into the page perpendicular to the velocity vector. Thus magnetic field must ...

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