A charged sphere has a mass of 850 g. The sphere enters a region that contains a

Question

A charged sphere has a mass of 850 g. The sphere enters a region that contains a magnetic field and an electric field. The electric field is measured to be 700 N/C and is pointed in the positive y-direction (top of the page). The magnetic field, which has a strength of 0.115 T, is pointed in the negative z-direction (into the page). The sphere, as it enters the region, is travelling in the positive x-direction (right of the page) with a speed of 500 m/s. What must the charge of the sphere be for the acceleration of the sphere in this region to be zero?

Explanation / Answer

Let the charge on the sphere be +Q coulombs

Force on sphere due to electric field = 700 Q Newtons along +y direction

Force on sphere due to magnetic firld(-z direction) F = Q (V X B)

velocity is along +x and field along -z => V X B is along +y direction

The forces due to electric and magnetic field add up instead of cancelling each other out.

Similarly for a - Q charge.

THUS THERE IS NO VALUE OF CHARGE SUCH THAT THE SPHERE CAN EXPERIENCE ZERO FORCE (ACCELERATION)

The forces due to electric & magntetic field always add up

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