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An isolated spherical conductor is charged - AQA - A-Level Physics - Question 18 - 2021 - Paper 2

Question 18

An isolated spherical conductor is charged. The conductor has a radius $R$ and an electric potential $V$. The electric field strength at its surface is $E$. Point ... show full transcript

Worked Solution & Example Answer:An isolated spherical conductor is charged - AQA - A-Level Physics - Question 18 - 2021 - Paper 2

Step 1

Electric field strength at T

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Answer

The electric field strength ( $E_T$ ) at a distance $d$ from the center of a charged spherical conductor is given by the formula:

$E_T = \frac{E}{k^2}$

where $k$ is a factor related to the distance; at point T, which is $2R$ away from the surface (i.e., $3R$ from the center), the electric field strength is:

$E_T = \frac{E}{(3)^2} = \frac{E}{9}$ .

Step 2

Electric potential at T

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Answer

The electric potential ( $V_T$ ) at point T can be found considering that the potential decreases with distance. The potential at point T is given by:

$V_T = V - E_T \times 2R$

Substituting $E_T$ :

$V_T = V - \frac{E}{9} \times 2R.$

However, as the distance is large, we can summarize the potential at point T:

$V_T = \frac{V}{3}.$

Thus, for point T at distance $2R$ , we expect: $V_T = \frac{V}{9}.$

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