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Consider two points 1 and 2 in a region ...

Consider two points `1 and 2` in a region outside a charged sphere. Two points are not very far away from the sphere. If `E and V` respresent the electric fileld vector and the electric potential. Which of the following is not possible ?

A

`|vec(E)_(1)|=|vec(E)_(2)|,V_(1)=V_(2)`

B

`vec(E)_(1)nevec(E)_(2),V_(1)neV_(2)`

C

`vec(E)_(1)nevec(E)_(2),V_(1)=V_(2)`

D

`|vec(E)_(1)|=|vec(E)_(1)|,V_(1) ne V_(2)`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the relationship between electric field (E) and electric potential (V) in the context of two points (1 and 2) outside a charged sphere. ### Step-by-step Solution: 1. **Understanding Electric Field and Electric Potential**: - The electric field (E) at a point in space due to a charged object is a vector quantity that represents the force per unit charge experienced by a positive test charge placed at that point. - The electric potential (V) at a point is a scalar quantity that represents the work done in bringing a unit positive charge from infinity to that point against the electric field. 2. **Equipotential Surfaces**: - An equipotential surface is a surface where the electric potential is the same at every point. This means that if two points lie on the same equipotential surface, their potentials (V1 and V2) will be equal (V1 = V2). - The electric field (E) is always perpendicular to the equipotential surfaces. Therefore, if two points are on the same equipotential surface, the electric field at those points can be equal (E1 = E2). 3. **Analyzing the Given Options**: - **Option 1**: If E1 = E2, then V1 must equal V2 (both points are on the same equipotential surface). This is possible. - **Option 2**: If E1 ≠ E2, it is possible for V1 to equal V2. This can occur if the points are at different distances from the charge but still have the same potential due to the nature of electric fields. - **Option 3**: If E1 ≠ E2, it is also possible for V1 ≠ V2. This is straightforward as different electric fields generally correspond to different potentials. - **Option 4**: If E1 = E2, then V1 cannot be different from V2. This is not possible because equal electric fields imply equal potentials if they are on the same equipotential surface. 4. **Conclusion**: - The option that is not possible is **Option 4**: If E1 = E2, then V1 cannot be different from V2. ### Final Answer: The option that is not possible is **Option 4**. ---
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