Q.

A non-conducting sheet of thickness d and large surface area contains a uniformly distributed charge of density ρ throughout its volume. The electric field at a point P (deep inside the sheet far away from all corners) inside the sheet at a distance x from the central plane is E1. Now the sheet is rolled to form a large solid cylinder. Field at a point P inside the cylinder at a distance x from its axis is  E2. Find the ratio E1E2
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answer is 2.

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Detailed Solution

E1=ρε0x E1=ρε0x    E2=ρ2ε0x  

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A non-conducting sheet of thickness d and large surface area contains a uniformly distributed charge of density ρ throughout its volume. The electric field at a point P (deep inside the sheet far away from all corners) inside the sheet at a distance x from the central plane is E1. Now the sheet is rolled to form a large solid cylinder. Field at a point P inside the cylinder at a distance x from its axis is  E2. Find the ratio E1E2