After the slab is charged, and the electrophorus is placed on the slab, the student briefly touches the electrophorus, effectively grounding it. After that, the electrophorus appears to be charged. By what method is it charged?

By induction method

Explanation:

Induction method involves charging an electrically neutral body by bringing it in contact with an electrically charged body.

For the electrophus, a charge opposite that on the slab is induced on the side in contact with the slab; driving the opposite charge (this will be the same as that on the slab) to the other end of the elctrophus. Touching the electrophus removes the charge opposite the charge induced on the electrophus by the charged slab either by drawing up charge from the earth or taking the charge to earth (depends on the charge. A negative charge is drawn to earth while a positive charge draws up electrons from the earth)

the higher the current the higher the mag field around it the higher the influence on the compass

i would say