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This question has statement 1 and statement 2.  Of the four choices given after the statements, choose the one that best describes the two statements.

An insulating solid sphere of radius R has a uniformly positive charge density  \rho . As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinity is zero.

Statement 1 : When a charge q is taken from the centre to the surface of the sphere, its potential energy changes by  \frac{qp}{3\varepsilon _{0}}

Statement 2 :  The electric field at a distance r(r < R) from the centre of the sphere is \frac{\rho r}{3\varepsilon _{0}}

 

  • Option 1)

    Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for statement 1.

  • Option 2)

    Statement 1 is true, Statement 2 is false

  • Option 3)

    Statement 1 is false, Statement 2 is true

  • Option 4)

    Statement 1 is true, Statement 2 is the correct explanation for statement 1

 

Answers (2)

best_answer

As we discussed in

If P lies at centre r = 0 -

V_{centre}=\frac{3}{2}\times \frac{1}{4\pi \epsilon _{0}}\frac{Q}{R}=\frac{3}{2}V_{s}

i.e         V_{c}> V_{s}> V_{o}

-

 

 Potential at the centre of the sphere,

V_{C}= \frac{R^{2}\rho }{2\varepsilon _{0}}

Potential at the surface of the sphere,

V_{S}= \frac{1}{3}\frac{R^{2}\rho }{\varepsilon _{0}}

When a charge q is taken from the centre to the surface, the change in potential energy is

\Delta U=\left ( V_{C} -V_{S}\right )q= \left (\frac{R^{2}\rho }{2\varepsilon _{0}} -\frac{1}{3}\frac{R^{2}\rho }{\varepsilon _{0}} \right )q= \frac{1}{6}\frac{R^{2}\rho q}{\varepsilon _{0}}

Statement 1 is false. Statement 2 is true.


Option 1)

Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for statement 1.

Option 2)

Statement 1 is true, Statement 2 is false

Option 3)

Statement 1 is false, Statement 2 is true

Option 4)

Statement 1 is true, Statement 2 is the correct explanation for statement 1

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