Why Is There No Normal Force on the Second Block in Contact Systems?

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If there are 2 blocks beside each other and a force is applied to the first block, the first block will push the second block has well. This means that the two blocks are in contact. So why isn't there a normal force drawn perpendicular to the side of the second block if it is in contact with another surface other than the ground?
 
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The blocks interact at the sides in contact. There is a normal force from the first block to the second one, and also a normal force, of equal magnitude and opposite direction, from the second block on the first one.

ehild
 
Ok so if the blocks were A and B, then F(A on B) and F(B on A) are actually the normal forces from the contact?