Question

two opposite corners of a square carry Q charge each and the other two opposite corners of the same square carry q charge each. if the resultant force on q is zero,how are Q and q related.

Answer 1

Given: Two opposite corners of a square carry Q charge each and the other two opposite corners of the same square carry q charge each.

To find: How are Q and q related?

Solution:

• Now we have given two corners are having q charge and other two corners are having Q charge.

• Now, let the side of square be x, then its diagonal will be: x√2

• Now forces are:

                   F1 = F2 = kQq / x²

                   F3 = F4 = kqq (x√2)² = kq² / 2x²

• Now we know that F1 ⊥ F2, so resultant will be:

                   F = √F1² + F2² = F1√2 (as F1 and F2 are equal)

• Now net force on q is 0, so:

                   F1√2 = -F3

                   kQq√2 / x² = -kq² / 2x²

• Cancelling the common terms, we get:

                   q = -2√2Q

Answer:

               So the relation between q and Q is q = -2√2Q