A positive charge +q is placed at the centre of a hollow metallic sphere of inner radius a and outer radius b. The electric field at a distance r from the centre is denoted by E. In this regard, which one of the following statements is correct ?

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Q: 93 (NDA-I/2017)
A positive charge +q is placed at the centre of a hollow metallic sphere of inner radius a and outer radius b. The electric field at a distance r from the centre is denoted by E. In this regard, which one of the following statements is correct ?

question_subject: 

Science

question_exam: 

NDA-I

stats: 

0,4,3,4,2,1,0

keywords: 

{'electric field': [0, 0, 0, 1], 'hollow metallic sphere': [0, 0, 0, 1], 'inner radius': [0, 0, 0, 1], 'centre': [10, 3, 7, 19]}

Option 1 is correct. When a positive charge +q is placed at the center of a hollow metallic sphere, the electric field inside the sphere is always zero. This is because the charges in the metallic sphere redistribute themselves in such a way that they cancel out the electric field inside. So, for r < a (inside the sphere), the electric field is zero.

However, for a < r < b (between the inner and outer radius of the sphere), the electric field is non-zero and is equal to +Q. This is because the charges on the inner surface of the sphere will produce an electric field pointing outward, and the charges on the outer surface will produce an electric field pointing inward. These two electric fields cancel each other out everywhere except between the inner and outer radius, where they add up to give a net electric field of +Q.

Therefore, option 1 is correct, stating that the electric field E is equal to +Q for a < r < b. Options 2, 3, and 4 are incorrect in the context of this scenario.