When a certain inductor carries a current I it stores 300 mJ

When a certain inductor carries a current I, it stores 3.00 mJ of magnetic energy. How much current (in terms of I) would it have to carry to store 9.00 mJ of energy?

Solution

Energy stored in an inductor W is proportianal to I^2 that is square of current. So for 3 mJ energy if current needed is I then for 9 mJ which is 3*3 mJ that is 3 times the earlier stored energy, then the current should be (3)^1/2 that is root 3 times the earlier current. So I (prime)= (3)^0.5 times I