A hollow metal sphere of radius 2 cm is charged such that the potential on its surface is 5 volts. The potential at the centre of the sphere is?

1. A

   5 volts

2. B

   Zero

3. C

   Same as at a point 2 cm away from the surface

4. D

   None of these

Appeared in: KPSC Staff Nurse - 2016

Explanation

• For any hollow conducting sphere in electrostatic equilibrium, all excess charge resides on its outer surface.
• A fundamental property of conductors in equilibrium is that the electric field inside the conductor is zero.
• Since the electric field is the gradient of potential (E = -dV/dr), a zero electric field means the potential is constant throughout the interior of the sphere.
• This constant potential inside the sphere is equal to the potential on its surface.
• Given the surface potential is 5 volts, the potential at any point inside, including the center, must also be 5 volts.

Why Other Options Were Wrong

• Option B: The potential inside a charged conductor is constant and equal to the surface potential, not necessarily zero.
• Option C: This point is located at r = 4 cm from the center. Outside the sphere, the electric potential decreases with distance (V ∝ 1/r). Therefore, the potential at 4 cm is less than the potential at the surface (r = 2 cm).
• Option D: This option is incorrect because a correct answer (5 volts) is present among the choices.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Electric potential of a hollow conducting sphere as background academic context rather than a clinical decision trigger.
• The principle that the electric field inside a hollow conductor is zero is known as electrostatic shielding.
• This concept is the basis for the Faraday cage, which is used to protect sensitive electronic equipment from external electromagnetic fields.
• In a medical context, MRI (Magnetic Resonance Imaging) rooms are constructed as Faraday cages to prevent external radiofrequency signals from interfering with the weak radiofrequency signals produced by the patient's body, which are necessary to create the image.

How to Approach the Question

• Identify the key object in the question: a 'hollow metal sphere'. Recognize that 'metal' implies it is a conductor.
• Recall the fundamental properties of a conductor in electrostatic equilibrium. The most important one here is that the electric field inside the conductor is zero.
• Understand the relationship between electric field (E) and electric potential (V). The field is the negative gradient of the potential (E = -dV/dr).
• Conclude that if E=0 inside the sphere, the potential V must be constant everywhere inside it.
• Equate the constant internal potential to the potential at the boundary, which is the surface of the sphere.
• Use the value given for the surface potential (5 volts) to determine the potential at the center.

Concept Tested & Keywords

• Concept Tested: Electric potential of a hollow conducting sphere
• Stem keywords: hollow metal sphere, radius 2 cm, potential on its surface, 5 volts, potential at the centre
• Lead-in keywords: is?

Question ID

QKqgwYQj3fBWPzAcyeIunj

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