SATHEE: Electrostatics Question 695

Electrostatics Question 695

Question: Two identical beads each have a mass m and charge q. When placed in a hemispherical bowl of radius R with frictionless, nonconductive walls, the beads move, and at equilibrium the distance between them is R (Fig.). Determine the charge on each bead.

Options:

A) $R {(\frac{m g}{k_{e} \sqrt{3}})}^{1 / 2}$

B) $R {(\frac{m g}{k_{e} \sqrt{2}})}^{1 / 2}$

C) $R {(\frac{m g}{k_{e} 2 \sqrt{3}})}^{1 / 2}$

D) $R {(\frac{2 m g}{k_{e} \sqrt{3}})}^{1 / 2}$

Show Answer

Answer:

Correct Answer: A

Solution:

[a] The bowl exerts a normal force N on each bead, directed along the radial line or at

$60.0^{\circ}$ above the horizontal.

Consider the free-body diagram of the bead on the left with electric force $F_{e}$ applied: $Σ F_{y} = N \sin 60^{\circ} - m g = 0$

$\Rightarrow N = \frac{m g}{\sin 60^{\circ}}$

$Σ F_{x} = - F_{e} + N \cos 60^{\circ} = 0$

$\Rightarrow \frac{k_{e} q^{2}}{R^{2}} = N \cos 60^{\circ} = \frac{m g}{\tan 60^{\circ}} = \frac{m g}{\sqrt{3}}$

$k_{e} = \frac{1}{4 π ε_{0}} \approx 9.0 \times 10^{9} N m^{2} / C^{2} ∴ q = R {(\frac{m g}{k_{e} \sqrt{3}})}^{1 / 2}$

Electrostatics Question 695

Question: Two identical beads each have a mass m and charge q. When placed in a hemispherical bowl of radius R with frictionless, nonconductive walls, the beads move, and at equilibrium the distance between them is R (Fig.). Determine the charge on each bead.

Options:

Answer:

Solution:

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Electrostatics Question 695

Question: Two identical beads each have a mass m and charge q. When placed in a hemispherical bowl of radius R with frictionless, nonconductive walls, the beads move, and at equilibrium the distance between them is R (Fig.). Determine the charge on each bead.

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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