Solve this following
Question: Find $\frac{d y}{d x}$, when: $y=x^{x \cos x}+\left(\frac{x^{2}+1}{x^{2}-1}\right)$ Solution:...
Read More →The plates of a parallel-plate capacitor are made of circular
Question: The plates of a parallel-plate capacitor are made of circular discs of radii $5.0 \mathrm{~cm}$ each. If the separation between the plates is $1.0 \mathrm{~mm}$, what is the capacitance? Solution:...
Read More →When 1.0×1012.electrons are transferred from one conductor to another,
Question: When $1.0 \times 10^{12}$.electrons are transferred from one conductor to another, a potential difference of $10 \mathrm{~V}$ appears between the conductors. Calculate the capacitance of the two-conductor system. Solution:...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when: $y=(\sin x)^{x}+\sin ^{-1} \sqrt{x}$ Solution:...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when: $y=(x \cos x)^{x}+(x \sin x)^{1 / x}$ Solution:...
Read More →Three identical metal plates with large surface areas are kept
Question: Three identical metal plates with large surface areas are kept parallel to each other as shown in figure. The leftmost plate is given a charge $Q$, the rightmost a charge $-2 Q$ and the middle one remains neutral. Find the charge appearing on the outer surface of the Rightmost plate. Solution:...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when: $y=x^{\sin x}+(\sin x)^{\cos x}$ Solution:...
Read More →Two conducting Plates X and Y,
Question: Two conducting Plates $X$ and $Y$, each having large surface area A (on one side), are placed parallel to each other shown in figure. The plate $X$ is given a charge $Q$ whereas the other is neutral. Find (a) the surface charge density at the inner surface of the plate $X$, (b) the electric field at a point to the left of the plates, (c) the electric field at a point in between the plates and (d) the electric field at a point to the right of the plates. Solution:...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when: $y=(\log x)^{x}+x^{\log x}$ Solution:...
Read More →Two large conducting plates are placed parallel to each other
Question: Two large conducting plates are placed parallel to each other and they carry equal and opposite charges with surface density $\sigma$ as shown in figure. Find the electric field (a) at the left of the plates, (b) in between the plates and (c) at the right of the plates. Solution:...
Read More →Solve this following
Question: Find $\frac{\mathrm{dy}}{\mathrm{dx}}$, when: $y=x^{x}-2^{\sin x}$ Solution:...
Read More →Two large conducting plates are placed parallel to each other
Question: Two large conducting plates are placed parallel to each other with a separation of $2.00 \mathrm{~cm}$ between them. An electron starting from rest near one of the plates reaches the other plate in $2.00$ microseconds. Find the surface charge density on the inner surfaces. Solution:...
Read More →Consider the situation of the previous problem.
Question: Consider the situation of the previous problem. (a) Find the tension in the string in equilibrium. (b) Suppose the ball is slightly pushed aside and released. Find the time period of the small oscillations. Solution:...
Read More →One end of a 10cm long silk thread is fixed to a large vertical
Question: One end of a $10 \mathrm{~cm}$ long silk thread is fixed to a large vertical surface of a charged nonconducting plate and the other end is fastened to a small ball having a mass of $10 \mathrm{~g}$ and a charge of $4.0 \times 10^{-6} \mathrm{C}$. In equilibrium, the thread makes an angle of $60^{\circ}$ with the vertical. Find the surface charge density on the plate. Solution:...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when: $y=(1+x)\left(1+x^{2}\right)\left(1+x^{4}\right)\left(1+x^{6}\right)$ Solution:...
Read More →A charged particle having a charge of
Question: A charged particle having a charge of $-2.0 \times 10^{-6} \mathrm{C}$ is placed close to a nonconducting plate having a surface charge density $4.0 \times 10^{-6} \mathrm{C} / \mathrm{m}^{2}$. Find the force of attraction between the particle and the plate. Solution:...
Read More →A nonconducting sheet of large surface area and thickness
Question: A nonconducting sheet of large surface area and thickness $d$ contains uniform charge distribution of density p. Find the electric field at a point $\mathrm{P}$ inside the plate, at a distance ${ }^{x}$ from the central plane. Draw a qualitative graph of $E$ against $x$ for $0$ $\mathrm{x}\mathrm{d}$. Solution:...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when: $y=\frac{x \cos ^{-1} x}{\sqrt{1-x^{2}}}$ Solution:...
Read More →A long cylindrical volume contains a uniformly distributed charge of
Question: A long cylindrical volume contains a uniformly distributed charge of density $p$. Find the electric field at a point P inside the cylindrical volume at a distance ${ }^{x}$ from its axis. Solution:...
Read More →A long cylindrical wire carries a positive charge of linear density
Question: A long cylindrical wire carries a positive charge of linear density $2.0 \times 10^{-8} \mathrm{C} / \mathrm{m}$. An electron revolves around it in a circular path under the influence of the attractive electrostatic force. Find the kinetic energy of the electron. Note that is independent of the radius. Solution:...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when: $y=\frac{e^{x} \log x}{x^{2}}$ Solution:...
Read More →Find the magnitude of the electric field at
Question: Find the magnitude of the electric field at a point $4 \mathrm{~cm}$ away from a line charge of density $2 \times 10^{-6} \mathrm{C} / \mathrm{m}$. Solution:...
Read More →Consider the following very rough model of a beryllium atom.
Question: Consider the following very rough model of a beryllium atom. The nucleus has four protons and four neutrons confined to a small volume of radius $10^{-15} \mathrm{~m}$. The two $1 \mathrm{~s}$ electrons make a spherical charge cloud at an average distance of $1.3 \times 10^{-11} \mathrm{~m}$ from the nucleus, whereas the two 2 s electrons make another spherical cloud at an average distance of $5.2 \times 10^{-11} \mathrm{~m}$ from the nucleus. Find the electric field at (a) a point jus...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when: $y=\frac{x^{3} \sin x}{e^{x}}$ Solution:...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when: $y=\sin 2 x \sin 3 x \sin 4 x$ Solution:...
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