A rod of length L has a total charge Q distributed uniformly along its length.
Question: A rod of length $L$ has a total charge $Q$ distributed uniformly along its length. It is bent in the shape of a semicircle. Find the magnitude of the electric field at the centre of curvature of the semicircle. Solution:...
Read More →Positive charge Q is distributed uniformly over a circulating of
Question: Positive charge $Q$ is distributed uniformly over a circulating of radius $\mathrm{R}$. A particle having a mass $\mathrm{m}$ and a negative charge $q$, is placed on its axis at a distance $x$ from the centre. Find the force on the particle. Assuming $xR$, find the time period of oscillation of the particle if it is released from there. Solution: $\mathrm{T}=\sqrt{\frac{16 \pi^{3} e_{0} \mathrm{mR}}{\mathrm{qQ}}}$...
Read More →Two small spheres, each having a mass of 20g,
Question: Two small spheres, each having a mass of $20 \mathrm{~g}$, are suspended from a common point by two insulating strings of length $40 \mathrm{~cm}$ each. The spheres are identically charged and the separation between the balls at equilibrium is found to be $4 \mathrm{~cm}$. Find the charge on each sphere. Solution:...
Read More →Two identical pith balls are charged by rubbing against each other.
Question: Two identical pith balls are charged by rubbing against each other. They are suspended from a horizontal rod through two strings of length $20 \mathrm{~cm}$ each, the separation between the suspension points being $5 \mathrm{~cm}$. In equilibrium, the separation points between the balls is $3 \mathrm{~cm}$. Find the mass of each ball has a magnitude $2.0 \times 10^{-8} \mathrm{c}$. Solution:...
Read More →Solve this following
Question: Find, when: $\left(x^{2}+y^{2}\right)^{2}=x y$ Solution:...
Read More →Two identical balls, each having a charge of
Question: Two identical balls, each having a charge of $2.00 \times 10^{-7} \mathrm{C}$ and a mass of $100 \mathrm{~g}$, are suspend from a common point by two insukating strings eacg $50 \mathrm{~cm}$ long. The balls are held at a separation $5.0 \mathrm{~cm}$ apart and then released. Find (a) the electric force on one of the charged balls (b) the components of the result force on it along and perpendicular to the string (c) the tension in the string (d) The acceleration of the balls. Answers a...
Read More →Two charged particles having charge
Question: Two charged particles having charge $2.0 \times 10^{-6}$ each are joined by an insulating string of length $1 \mathrm{M}$ and the system is kept on a smooth horizontal table. Find the tension in the string. Solution:...
Read More →Ten positively charged particles are kept fixed on the X-axis
Question: Ten positively charged particles are kept fixed on the X-axis at point $x=10 \mathrm{~cm}, 20 \mathrm{~cm}, 30 \mathrm{~cm}, \ldots ., 100 \mathrm{~cm}$. The first particles have a charge $1.0^{\times 10^{-6}} \mathrm{C}$, the second $8^{\times 10^{-8}}$, and the third $27^{\times 10^{-8}} \mathrm{C}$ and so on. The tenth particle has a charge $1000^{\times 10^{-8}}$ C. Find the magnitude of the electric force acting on a $1 \mathrm{C}$ charge placed at the origin. Solution:...
Read More →Find the speed of the electron in the ground state of a hydrogen atom.
Question: Find the speed of the electron in the ground state of a hydrogen atom. The description of ground state is given in the previous problem. Solution:...
Read More →A hydrogen atom contains one proton and one electron.
Question: A hydrogen atom contains one proton and one electron. It may be assumed that the electron revolves in a piece rod radius $0.53$ angstrom ( 1 angstrom $=10^{-10} \mathrm{~m}$ and is abbreviated as $\mathrm{A}$ ) with the proton at the centre. The hydrogen atom is said to be in the ground state in this case. Find the magnitude of the electric force between the proton and the electron of a hydrogen atom in its ground state. Solution:...
Read More →Four equal charges
Question: Four equal charges $2.0 \times 10^{-6} \mathrm{C}$ each are fixed at the four corners of a square of side $5 \mathrm{~cm}$. Find the coulomb force experienced by one of the charges due to the rest three. Solution:...
Read More →Three equal charges , 2.0 ×10-6 C each,
Question: Three equal charges, $2.0 \times 10^{-6} \mathrm{C}$ each, are held fixed at the three corners of an equilateral triangles of side $5 \mathrm{~cm}$. Find the coulomb force experienced by one of the charges due to the rest two. Solution:...
Read More →Suppose an attractive nuclear force acts between two protons
Question: Suppose an attractive nuclear force acts between two protons which may be written as $\mathrm{F}=\mathrm{ce} \mathrm{ekr}^{-\mathrm{r}}{ }^{2}$. (a) Write down the dimensional formulae and appropriate SI units of C and $\mathrm{k}$ (b) Suppose that $k=1$ Fermi and that the repulsive electric force between the protons is just balanced by the attractive nuclear force when the separation is 5 Fermi. Find the value of $C$. Solution:...
Read More →Solve this following
Question: Find, when: $\sqrt{\mathrm{x}}+\sqrt{\mathrm{y}}=\sqrt{\mathrm{a}}$ Solution: Let us differentiate the whole equation w.r.t $x$ $\frac{d y}{d x}=\frac{-\sqrt{y}}{\sqrt{x}}$...
Read More →Find the ratio of the electric and gravitational forces
Question: Find the ratio of the electric and gravitational forces between two protons. Solution:...
Read More →NaCl molecule is bound due to the electric force between
Question: $\mathrm{NaCl}$ molecule is bound due to the electric force between the sodium and the chlorine ions when one electron of sodium is transferred to chlorine. Taking the separation between the ions to be $2.75^{\times 10^{-8}} \mathrm{~cm}$, find the force of attraction between them. State the assumptions (if any) that you have made. Solution:...
Read More →Two insulating small spheres are rubbed against each other
Question: Two insulating small spheres are rubbed against each other and placed $1 \mathrm{~cm}$ apart. If they attract each other with a force of $0.1 \mathrm{~N}$, how many electrons were transferred from one sphere to the other during rubbing? Solution:...
Read More →Consider a gold nucleus to be a sphere of radius
Question: Consider a gold nucleus to be a sphere of radius $6.9$ Fermi in which protons and neutrons are distributed. Find the force of repulsion between two protons situated at largest separation. Why do these protons not fly apart under this repulsion? Solution:...
Read More →Suppose all the electrons in 100g of water are lumped together
Question: Suppose all the electrons in $100 \mathrm{~g}$ of water are lumped together to form a negatively charged particle and all the nuclei are lumped together to form a positively charged particle. If these two particles are placed $10.0 \mathrm{~cm}$ away from each other, find the force of attraction between them. Compare it with your weight. Solution:...
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