A sample of HCL gas is placed in an electric field of
Question: A sample of HCL gas is placed in an electric field of $2.5^{\times 10^{4}} \mathrm{~N} / \mathrm{C}$. The dipole moment if each HCL molecule is $3.4^{\times 10^{-30}}$ C$\mathrm{m}$. Find the maximum torque that can act on a molecule. Solution:...
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Question: Find $\frac{d y}{d x}$, when $y=(x+1)^{3}(x+2)^{4}(x+3)^{5}$ Solution:...
Read More →Two particles have equal masses of
Question: Two particles have equal masses of $5.0 \mathrm{~g}$ each and opposite charges of $+4.0^{\times 10^{-5}} \mathrm{C}$ and $-4.0^{\times} 10^{-5} \mathrm{C}$. They are released from rest with separation of $1.0 \mathrm{~m}$ between them. Find the speeds of the particles when the separation is reduced to $50 \mathrm{~cm}$. Solution:...
Read More →Two identical particles, each having a charge of
Question: Two identical particles, each having a charge of $2.0^{\times 10^{-4}} \mathrm{C}$ and mass of $10 \mathrm{~g}$, are kept at a separation of $10 \mathrm{~cm}$ and then released. What would be the speeds of the particles when the separation becomes large? Solution:...
Read More →The kinetic energy of a charged particle decreases by
Question: The kinetic energy of a charged particle decreases by $10 \mathrm{~J}$ as it moves from a point at potential $100 \mathrm{~V}$ to a point at potential $200 \mathrm{~V}$. Find the charge on the particle. Solution:...
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Question: Find $\frac{d y}{d x}$, when: $y=(3 x+5)^{(2 x-3)}$ Solution:...
Read More →How much work has to be done in assembling three charged
Question: How much work has to be done in assembling three charged particles at the verticals of an equilateral Triangle as shown in figure $(29-E 5)$ ? Solution:...
Read More →A uniform field of 2.0N/C exists in space in x-direction.
Question: A uniform field of $2.0 \mathrm{~N} / \mathrm{C}$ exists in space in x-direction. (a) Taking the potential at the origin to be zero, write an expression for the potential at a general point ( $x, y, z$ ). (b) At which points, the potential is $25 \mathrm{~V}$ ? (c) If the potential at the origin is taken to be $100 \mathrm{~V}$, what will be the expression for the potential at a general point? (d) What will be the potential at the origin if the potential at infinity is taken to be zero...
Read More →An electric field of magnitude 1000N/C is produced
Question: An electric field of magnitude $1000 \mathrm{~N} / \mathrm{C}$ is produced between two parallel plates having a separation of $2.0 \mathrm{~cm}$ as shown in figure (29-E4). (a) What is the potential difference between the plates? (b) With what minimum speed should an electron be projected from the lower plate in the direction of the field so that it may reach the upper plate? (c) Suppose the electron is projected from the lower plate with the speed calculated in part (b). The direction...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when: $y=\sin \left(x^{x}\right)$ Solution:...
Read More →Consider a circular ring of radius r,
Question: Consider a circular ring of radius $\mathrm{r}$, uniformly charged with linear charge density. Find the electric potential at a point on the axis at a distance $x$ from the centre of the ring. Using this expression for the potential, find the electric field at this point. Solution: $\mathrm{E}=\frac{\mathrm{r} \lambda \mathrm{x}}{2 \mathrm{e}_{0}\left(\mathrm{r}^{2}+\mathrm{x}^{2}\right)^{3 / 2}}$...
Read More →Some equi potential surfaces are shown in figures (29.E3).
Question: Some equi potential surfaces are shown in figures (29.E3). What can you say about the magnitude and the direction of the electric field? Solution:...
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Question: Find $\frac{d y}{d x}$, when: $y=\left(\sin ^{-1} x\right)^{x}$ Solution:...
Read More →Two charged particles,
Question: Two charged particles, having equal charges of $2.0^{\times 10^{-5}}$ each are brought from infinity to within a separation of $10 \mathrm{~cm}$. Find the increase in the electric potential energy during the process. Solution:...
Read More →The electric potential existing in space is
Question: The electric potential existing in space is $v(x, y, z)=A(x y+y z+z x)$. (a) Write the dimensional formula of A. (b) Find the expression for the electric field. (c) If $A$ is $10 S I$ units, find the magnitude of the electric field at $(1 \mathrm{~m}, 1 \mathrm{~m}, 1 \mathrm{~m})$. Solution:...
Read More →An electric field
Question: An electric field $\vec{E}=\vec{i}_{\text {Ax exists in }}$ the space, where $A=10 \mathrm{~V} / \mathrm{m}^{2}$ Take the potential at $(10 \mathrm{~m}, 20 \mathrm{~m})$ to be zero. Find the potential at the origin. Solution:...
Read More →An electric field
Question: An electric field $\left.\overrightarrow{\mathrm{E}}_{=} \overrightarrow{\mathrm{i}}_{20}+\overline{\mathrm{J}}_{30}\right) \mathrm{N} / \mathrm{C}$ exists in the space. If the potential at the origin is taken to be zero, find the potential at Solution:...
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Question: Find $\frac{\mathrm{dy}}{\mathrm{dx}}$, when: $y=x^{\sin 2 x}$ Solution:...
Read More →Consider the situation of the previous problem.
Question: Consider the situation of the previous problem. A charge of $-2.0^{\times 10^{-4}} \mathrm{C}$ is moved from the point $A$ to the point $B$. Find the change in electrical potential energy $\mathrm{U}_{\mathrm{B}}-\mathrm{U}_{\mathrm{A} \text { for }}$ the cases (a),(b)and (c). Solution:...
Read More →An electric field of 20 N/C exists along the X-axis in space.
Question: An electric field of $20 \mathrm{~N} / \mathrm{C}$ exists along the $\mathrm{X}$-axis in space. Calculate the potential difference $\mathrm{V}_{\mathrm{B}}-\mathrm{v}_{\mathrm{B}}$ where the points $\mathrm{A}$ and $\mathrm{B}$ are given by, (a) $A=(0,0) ; B=(4 m, 2 m)$ (b) $A=(4 m, 2 m) ; B=(6 m, 5 m)$ (c) $A=(0,0) ; B=(6 m, 5 m)$. Do you find any relation between the answers of parts (a), (b)and (c)? Solution:...
Read More →Two equal charges,
Question: Two equal charges, $2.0^{\times 10^{-7}}$ C each, are held fixed at a separation of $20 \mathrm{~cm}$. A third charge of equal magnitude is placed midway between the two charges. It is now moved to a point $20 \mathrm{~cm}$ from both the charges. How much work is done by the electric field during the process? Solution:...
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Question: Find $\frac{d y}{d x}$, when: $y=(\tan x)^{\cot x}$ Solution:...
Read More →12J of work has to be done against anexisting electric field to take charge of
Question: $12 \mathrm{~J}$ of work has to be done against anexisting electric field to take charge of $0.01 \mathrm{C}$ from $\mathrm{A}$ to $\mathrm{B}$. How much is the potential difference $v_{B}-v_{B}$ ? Solution:...
Read More →A uniform electric field of 10 N/C exists in the vertically downward direction.
Question: A uniform electric field of $10 \mathrm{~N} / \mathrm{C}$ exists in the vertically downward direction. Find the increase in the electric potential as one goes up through a height of $50 \mathrm{~cm}$. Solution:...
Read More →A block of mass m containing a net positive charge q is placed
Question: A block of mass $m$ containing a net positive charge $q$ is placed on a smooth horizontal table which terminates in a vertical wall as shown in figure (29-E2). The distance of the block from the wall is $\mathrm{d}$. A horizontal electric field $E$ towards right is switched on. Assuming elastic collisions (if any) find the time period of the resulting oscillatory motion. Is it a simple harmonic motion? Solution:...
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