Question

A clock face has charges $-q,-2q,-3q,...-12q$ fixed at the position of the corresponding numbers on the dial. The clock hands do not disturb the net field due to the point charges. Then, at what time does the hour hand point in the direction of the electric field at the centre of the dial?

• A. $8:30$
• B. $9:30$
• C. $10:30$
• D. $11:30$

Answer 1

The correct option is B $9:30$

The net electric field due to the oppositely faced charges would be in the direction of $-7q,-8q,-9q,-10q,-11q$ and $-12q$ and the magnitude of these charges would be $-6q$ each.

The resultant of $-10q,-11q$ and $-12q$ would point in the direction of $-11q$ and the resusltant of $-7q,-8q$ and $-9q$ would point in the direction of $-8q$.

Now finally the resultant of $-11q$ and $-8q$ would point in the direction of $9:30.$

$\text{Alertnative method:}$
Let, electric field at $1$ be $E_1$. The direction of individual fields and the net field due to opposite corner charges are as depicted below.


We notice that the resultant field will be along angle bisector of field between $9$ and $10$.
Therefore, answer will be $9:30$.