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If some charge is given to a conducting ...

If some charge is given to a conducting object of any shape, then match the following columns, under electrostatic condition
`{:(,"Column I",,"Column II"),((A),vec(E)" at a point within conducting material",(p),"Must be zero"),((B),vec(E)"at a point outside the material ",(q),"May be Zero"),((C ),vec(E)"at a point in a cavity having no charge",(r ),"May be uniform but not zero"),((D),vec(E)"at a point in the cavity having some charge",(s),"May be non-uniform"),(,,(t),"Cannot predict"):}`

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The correct Answer is:
To solve the problem of matching the electric field conditions in a conducting object with the given options, we can analyze each part step by step. ### Step-by-Step Solution: 1. **Electric Field at a Point Within Conducting Material (A)**: - In a conductor at electrostatic equilibrium, the electric field inside the conducting material is always zero. This is because the charges redistribute themselves on the surface of the conductor, and any electric field would cause further movement of charges until equilibrium is reached. - **Conclusion**: A matches with P (Must be zero). 2. **Electric Field at a Point Outside the Material (B)**: - The electric field just outside a charged conductor can be calculated using Gauss's law. However, if there are other conductors nearby, their electric fields can cancel each other out, leading to a situation where the electric field outside may be zero. - **Conclusion**: B matches with Q (May be Zero). 3. **Electric Field at a Point in a Cavity Having No Charge (C)**: - If there is a cavity inside a conductor and there is no charge present in that cavity, the electric field inside that cavity is also zero. This is due to the fact that the charges on the conductor's surface will create an opposing electric field that cancels out any field within the cavity. - **Conclusion**: C matches with P (Must be zero). 4. **Electric Field at a Point in a Cavity Having Some Charge (D)**: - If there is a charge present in the cavity, the electric field can vary. It may be zero if the charge distribution is such that the fields cancel out, but it can also be non-uniform depending on the configuration of the charges. - **Conclusion**: D matches with S (May be non-uniform). ### Final Matching: - A → P (Must be zero) - B → Q (May be Zero) - C → P (Must be zero) - D → S (May be non-uniform)
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