$($a$)$ What is the direction $($left to right, or right to left$)$ of the induced current through the resistor of Figure $4($a$)$ when the bar magnet is moved out of the coil? Is the right side of the coil a North pole or a South pole? Justify your answers.

$($b$)$ If the resistance $R$ in the left$-$hand circuit of Figure $4($b$)$ is increased, what is the direction $($clockwise or counter$-$clockwise$)$ of the induced current in the right$-$hand circuit? Justify your answer.

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