Question

Two point charges, $Q_1=+5C$ and $Q_2=-2C$, are placed inside a hollow conducting sphere that has radius 5 cm. The charges are arranged as shown in the diagram. Point A is located outside the conducting sphere 10 cm from the center of the sphere.
Which of the following actions will increase the magnitude of the electric field at point A?
I: Reversing the placement of charges $Q_1$ and $Q_2$. II: Replacing the sphere with a larger one that has radius of 8 cm III: Replacing $Q_1$ and $Q_2$ with two other charges, $Q_3=-18C$ and $Q_4=+21C$

• A. I only
• B. II only
• C. III only
• D. I, II and III
• E. None of these actions will increase the magnitude of electric field at point A.

Answer 1

The correct option is A I only

Electric field at A increases due to positive charge and decreases due to negative charge. $Q_1=+5C$ creates field at A and $Q_2$ reduces its strength. By swapping their places, the positive charge will be closer to A and negative one will be away. Hence field strength will increase, $I:$ is applicable.

The positive charge (being stronger than the negative) is causing induction and the outer surface of the sphere is positive. This further increases the field at A. If the sphere is replaced with a larger one, the outer surface will be closer to A, but because the inner surface will be further the induction will reduce. Hence this won't cause any significant difference. Hence $II:$ is not applicable.

$III:$ is not applicable because although the charges are greater, the difference between them is the same. Hence field intensity will remain same.