A small sphere whose mass is 0.1 gm carries a charge of 3 ×10^-10 C and is tie up to one end of

step 1 Hi friends, here it is given a small sphere of mass 0 .1 gram, that is 10 to the power minus 4 k

A small sphere whose mass is 0.1 gm carries a charge of 3...

A small sphere whose mass is $0.1 \mathrm{gm}$ carries a charge of $3 \times 10^{-10} \mathrm{C}$ and is tie up to one end of a silk fiber $5 \mathrm{~cm}$ long. The other end of the fiber is attached to a large vertical conducting plate which has a surface charge of $25 \times 10^{-6} \mathrm{Cm}^{-2}$, on each side. When system is freely hanging the angle fiber makes with vertical is $\ldots \ldots \ldots$ (A) $41.8^{\circ}$ (B) $45^{\circ}$ (C) $40.2^{\circ}$ (D) $45.8^{\circ}$

A small sphere whose mass is $0.1 \mathrm{gm}$ carries a charge of $3 \times 10^{-10} \mathrm{C}$ and is tie up to one end of a silk fiber $5 \mathrm{~cm}$ long. The other end of the fiber is attached to a large vertical conducting plate which has a surface charge of $25 \times 10^{-6} \mathrm{Cm}^{-2}$, on each side. When system is freely hanging the angle fiber makes with vertical is $\ldots \ldots \ldots$
(A) $41.8^{\circ}$
(B) $45^{\circ}$
(C) $40.2^{\circ}$
(D) $45.8^{\circ}$

Key Concepts

Electric Field due to a Charged Conductor

A large, uniformly charged conducting plate creates a nearly uniform electric field in the region close to its surface. The field near an infinite charged sheet is given by E = ?/??, where ? is the surface charge density and ?? is the permittivity of free space. Understanding this helps in determining the force on a charge placed in such a field.

Gravitational Force

This is the force that acts on a mass due to gravity, calculated using F = mg, where m is the mass and g is the acceleration due to gravity. In equilibrium scenarios, the gravitational force is one of the forces that must be balanced by other forces, such as electric force and the tension in a supporting string.

Equilibrium of Forces

In static equilibrium, the net force acting on an object is zero. This principle is used to set up equations that balance the gravitational force, the electrostatic force, and the tension in the fiber. Resolving these forces into components allows for the determination of angles or other unknown quantities in the system.

Electrostatic Force

This concept involves the force experienced by a charged object placed in an external electric field. The magnitude of the force is given by F = qE, where q is the charge of the object and E is the electric field strength. In equilibrium problems, this force is balanced against other forces such as gravity.

Transcript

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