In Shakespeare's play Julius Caesar, what are Brutus' internal and external conflicts?

In the play Julius Caesar, Brutus has many struggles – both internal and external. As for internal struggles, he is very divided. On the one hand, he genuinely loves Caesar. From a historical perspective, Caesar has been kind to Brutus. Caesar even pardoned him when he fought against him. In other words, Brutus has experienced Caesar's famous clementia. On the other hand, Brutus is beginning to believe that Caesar is a tyrant, which means...

In the play Julius Caesar, Brutus has many struggles – both internal and external. As for internal struggles, he is very divided. On the one hand, he genuinely loves Caesar. From a historical perspective, Caesar has been kind to Brutus. Caesar even pardoned him when he fought against him. In other words, Brutus has experienced Caesar's famous clementia. On the other hand, Brutus is beginning to believe that Caesar is a tyrant, which means that he has to do something to defend Rome.  Another struggle concerns Brutus’ family lineage. He is the direct descendent of another Brutus who drove out the last king.  So, there is the pressure of defending the Republic in a time of potential need (tyranny).

From an external perspective, Brutus feels the pressure of the other conspirators, especially Cassius.  The conspirators convince him that Caesar wants to be king, which belies the very fabric of the Republic.  To use the words of the play, Caesar is "a serpent's egg" and so he must be killed “in the shell.”  The same point can be made in view of the Republic itself. Brutus feels that he needs to defend the Republic.  If he does not, who will? 

One of the most famous quotes that show this struggle is as follows:

If there be any in this assembly, any dear 
friend of Caesar's, to him I say that Brutus' love 
to Caesar was no less than his. If then that friend 
demand why Brutus rose against Caesar, this is my 
answer: not that I loved Caesar less, but that I loved
 Rome more. (3.2.19-24)

This is why Brutus is the tragic hero of the play. He is the one who struggles the most and is probably the most genuine in terms motive.