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Physics Electric Charge and Field

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3 months ago

Physics Electric Charge and Field Class 12th

A particle of mass 1 mg and charge q is lying at the mid-point of two stationary particles kept at a distance 2 m when each is carrying same charge q'. If the free charged particle is displaced from its equilibrium position through distance 'x' (x << 1m). The particle executes SHM. Its angular frequency of oscillation will be ______ * 10? rad/s if q' = 1 C.

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Raj Pandey

Contributor-Level 9

F_net = -kq²/ (l+x)² + kq²/ (l-x)²
= kq² [ (l+x)² - (l-x)² / (l²-x²)² ]
= kq² [ 4lx / (l²-x²)² ]
For x << l,
ma ≈ -4kq²x / l³
a = - (4kq²/ml³)x
ω² = 4kq²/ml³
ω = √ (4kq²/ml³)
= √ (4 * 9*10? * 10 / (1*10? * 1)
= 6 * 10? rad/s
= 6000 * 10? rad/s

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3 months ago

Physics Electric Charge and Field Electric Charges and Fields

Two identical tennis balls each having mass 'm' and charge 'q' are suspended from a fixed point by threads of length 'l'. What is the equilibrium separation when each thread makes a small angle 'θ' with the vertical?

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Vishal Baghel

Contributor-Level 10

T sin θ = (1/4πε? ) * q²/ (2lsinθ)²
T cos θ = mg
∴ tan θ = q² / (4πε? mg * 4l²sin²θ)
[tan θ ≈ θ, for small angle]
So, θ³ = q² / (16πε? mgl²)
θ = ( q² / (16πε? mgl²) )¹/³
Also separation = 2l sin θ ≈ 2lθ
= 2l ( q² / (16πε? mgl²) )¹/³
= ( 8q²l³ / (16πε? mgl²) )¹/³
= ( q²l / (2πε? mg) )¹/³

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3 months ago

Physics Electric Charge and Field Electric Charges and Fields

An inclined plane making an angle of 30° with the horizontal is placed in a uniform horizontal electric field $200 \frac{N}{C}$ as shown in the figure. A body of mass 1kg and charge 5 mC is allowed to slide down from rest at a height of 1m. If the coefficient of friction is 0.2, find the time taken by the body to reach the bottom.

$[g = 9.8 m / s^{2}; s i n 30 ° = \frac{1}{2}; c o s 30 ° = \frac{\sqrt[]{3}}{2}]$

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Vishal Baghel

Contributor-Level 10

$N = m g c o s 30 ° + q E s i n 30 °$

$a = \frac{m g s i n θ - q E c o s θ - μ N}{m} = 2.30 m / s^{2}$

$S = u t + \frac{1}{2} a t^{2}$

$\Rightarrow t = \sqrt[]{\frac{2 l}{a}} = 1.31 s e c$

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3 months ago

Physics Electric Charge and Field Class 12th

Find the electric field at point P (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length L carrying a charge Q. The distance of the point P from the centre of the rod is a = $\frac{\sqrt[]{3}}{2} L .$

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Payal Gupta

Contributor-Level 10

$E = \frac{λ}{4 π ε_{0} a} [s i n α + s i n α] = \frac{λ s i n α}{2 π ε_{0} a}$

$\Rightarrow E = \frac{Q}{L 2 π ε_{0} * (\frac{\sqrt[]{3} L}{2})} * \frac{1}{2} = \frac{Q}{2 \sqrt[]{3} π ε_{0} L^{2}}$

$t a n α = \frac{\frac{L}{2}}{\sqrt[]{3} L / 2} \Rightarrow α = \frac{π}{6} \Rightarrow s i n α = \frac{1}{2}$

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3 months ago

Physics Electric Charge and Field NCERT Solutions

Which is the best conducting material under room temperature?

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Piyush Vimal

Beginner-Level 5

The best conductor of electricity is Silver (Ag) at room temperature. It is not used in normal wiring even though being the best conductor because of its high cost.

Electrical Conductivity ( $\sigma$ ): $6.3 \times 10^ {7} \ \text {S/m}$
Electrical Resistivity ( $\rho$ ): $1.59 \times 10^ {-8} \ \Omega \cdot \text {m}$ (the lowest among all metals)

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3 months ago

Physics Electric Charge and Field Class 12th

A point charge of + $12 μ C$ is at a distance 6cm vertically above the centre of a squared of side 12cm as shown in figure. The magnitude of the electric flux through the square will be…………….* 10³ Nm²/C.

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Vishal Baghel

Contributor-Level 10

Flux through the 6 sides of square (i.e. cube)

$?_{T} = \frac{q_{i n}}{ε_{0}} = \frac{12 * 1 0^{- 6} C}{ε_{0}}$

$∴$ Flux through a square

$? = \frac{?_{T}}{6} = \frac{12 * 1 0^{- 6}}{ε_{0} * 6} = \frac{2 * 1 0^{- 6}}{ε_{0}}$

$\Rightarrow ? = 225.98 * 1 0^{3} N m^{2} / C ? 226 N m^{2} / C$

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3 months ago

Physics Electric Charge and Field Class 12th

A point charge of + $12 μ C$ is at a distance 6cm vertically above the centre of a squared of side 12cm as shown in figure. The magnitude of the electric flux through the square will be…………….× 10³ Nm²/C.

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New answer posted

3 months ago

Physics Electric Charge and Field Electric Charges and Fields

In an octagon ABCDEFGH of equal side, what is the sum of $\vec{A B} + \vec{A C} + \vec{A D} + \vec{A E} + \vec{A F} + \vec{A G} + \vec{A H},$ if,

$\vec{A O} = 2 \hat{i} + 3 \hat{j} - 4 \hat{k}$

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Vishal Baghel

Contributor-Level 10

$\vec{A B} + \vec{A H} = \vec{A O}$

$\vec{A C} + \vec{A G} = 2 \vec{A O}$

$\vec{A D} + \vec{A F} = 3 \vec{A O}$

$\vec{A E} = 2 \vec{A O}$

Adding All,

$\vec{A B} + \vec{A C} + \vec{A D} + \vec{A E} + \vec{A F} + \vec{A G} + \vec{A H} = 8 \vec{A O} = 16 \hat{i} + 24 \hat{j} - 32 \hat{k}$

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3 months ago

Physics Electric Charge and Field Class 12th

An electron with kinetic energy K₁ enters between parallel plates of a capacitor at an angle 'α' with the plates. It leaves the plates at angle 'β' with kinetic energy K₂. Then the ratio of kinetic energies K₁ : K₂will be

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