Test Index

Electrostatics

Section: Physics

Question : 22 of 59

Marks: +1, -0

\varepsilon_0

Solution:

Option-1:If

h = \frac{8R}{5}

and

r = \frac{3R}{5}

,the cylindrical surface just fits into the sphere. If

h < \frac{8R}{5}

, the cylindrical surface will be well inside the sphere.

\phi = \;\;\frac{q_{in}}{\varepsilon_0} = \;\;\frac{0}{\varepsilon_0} = 0

∴ (1) is correct

Option -2: If h>2R and r>R the sphere will be well inside the cylinder

\therefore \phi = \;\;\frac{Q}{E_{0}}

∴ (2) is correct

Option 3:

q_{in} = (Q_{AB})2

= \;\;\frac{Q}{2}(1 - \cos\theta) \times 2

= Q\left[1 - \;\;\frac{4}{5}\right] = \;\;\frac{Q}{5}

\therefore \phi = \;\;\frac{q_{in}}{\varepsilon_0} = \;\;\frac{Q}{5\varepsilon_0}

∴ (3) is correct

Option 4:

q_{in} = \;\;\frac{Q}{2}(1 - \cos 53^{\circ}) \times 2 = \frac{2Q}{5}

Q = \frac{2Q}{5}\varepsilon_0

∴(4) is wrong

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