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I had the following problem:

A proton is moving to the right at constant speed v and enters a region with uniform magnetic and electric fields. It continues to move in a straight line. The magnetic field is directed toward the top of the page. What is the direction of the electric field?

Using the right hand rule, with fingers pointed to the right and curled fingers up, my thumb points out of the page, leading me to believe that would be the answer. The correct answer is actually that the electric field points into the page. (I have received the answer to this question but not the explanation). Why is this?

Thank you!

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    $\begingroup$ You've found the direction of the magnetic force by the right hand rule. Why would you think the correct answer for the direction of the electric field is the direction of the magnetic force? $\endgroup$ – Alfred Centauri May 12 '18 at 2:19
  • $\begingroup$ Related? Have a read of the velocity selector here physics.stackexchange.com/q/287011/104696 $\endgroup$ – Farcher May 12 '18 at 4:10
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The correct answer is actually that the electric field points into the page. (I have received the answer to this question but not the explanation). Why is this?

So for this question, you have proved that the magnetic force acting on your moving charge points out of the page. For your charge to move on without deflecting, the net force acting upon it must be zero. In other words: $F_E$ + $F_B$ = $0$

The electric force has to act in a direction equal and opposite to the magnetic force. Therefore, your electric force must point into the page.

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