A charge Q is placed at the centre of an uncharged,
Question: A charge $\mathrm{Q}$ is placed at the centre of an uncharged, hollow metallic sphere of radius a' (a) Find the surface charge density on the inner surface and on the outer surface. (b) If a charge $q$ is put on the sphere, what would be the surface charge densities on the inner and the outer surfaces? (c) Find the electric field inside the sphere at a distance $x$ from the centre in the situations (a) and (b). Solution:...
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Question: Find $\frac{d y}{d x}$, when: $y=\sqrt{(x-2)(2 x-3)(3 x-4)}$ Solution:...
Read More →A charge Q is distributed uniformly within the material of
Question: A charge $\mathrm{Q}$ is distributed uniformly within the material of a hollow sphere of inner and outer radii $r_{1}$ and $r_{2}{ }^{\circ}$ Find the electric field at a point $\mathrm{P}$ a distance ${ }^{x}$ away from the centre for $\mathrm{r}_{1}\mathrm{x}\mathrm{r}_{2}$ Draw a rough graph showing the electric field as a function of $x$ for $0\mathrm{x}2 \mathrm{r}_{2}$. Solution:...
Read More →The radius of a gold nucleus (Z = 79) is about
Question: The radius of a gold nucleus $(\mathrm{Z}=79)$ is about $7.0 \times 10^{-15} \mathrm{~m}$. Assume that the positive charge is distributed uniformly throughout the nuclear volume. Find the strength of the electric field at (a) the surface of the nucleus and (b) at the middle point of a radius. Remembering that gold is a conductor, is it justified to assume that the positive charge is uniformly distributed over the entire volume of the nucleus and does not come to the outer surface? Solu...
Read More →A spherical volume contains a uniformly distributed charge of
Question: A spherical volume contains a uniformly distributed charge of density. $2.0 \times 10^{-4} \mathrm{C} / \mathrm{m}^{3}$. Find the electric field at a point inside the volume at a distance $4.0 \mathrm{~cm}$ from the centre. Solution:...
Read More →A charge Q is placed at the centre of an imaginary hemispherical surface.
Question: A charge $Q$ is placed at the centre of an imaginary hemispherical surface. Using symmetry arguments and the Gauss's law, find the flux of the electric field due to this charge through the surface of the hemisphere. Solution:...
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Question: Find $\frac{d y}{d x}$, when: $y=\frac{x^{2} \sqrt{1+x}}{\left(1+x^{2}\right)^{3 / 2}}$ Solution:...
Read More →Find the flux of the electric field through a spherical surface of
Question: Find the flux of the electric field through a spherical surface of radius $\mathrm{R}$ due to a charge of $10^{-7} \mathrm{C}$ at the centre and another equal charge at a point $2 R$ away from the centre. Solution:...
Read More →A charge Q is placed at a distance a/2 above the centre of a horizontal,
Question: A charge $\mathrm{Q}$ is placed at a distance $\mathrm{a} / 2$ above the centre of a horizontal, square surface of edge $\alpha$ as shown in figure. Find the flux of the electric field through the square surface. Solution:...
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Question: Find $\frac{d y}{d x}$, when: $y=\frac{\sqrt{x}(3 x+5)^{2}}{\sqrt{x+1}}$ Solution:...
Read More →A charge Q is placed at the centre of a cube.
Question: A charge $Q$ is placed at the centre of a cube. Find the flux of the electric field through the six surfaces of the cube. Solution:...
Read More →The electric field in a region is given by
Question: The electric field in a region is given by $\vec{E}=\frac{E_{0} x}{l} i$. Find the charge contained inside a cubical volume bounded by the surfaces $x=0, x=a, y=a, z=0$ and $z=a$. Take $E_{0}=5 \times 10^{3} \mathrm{~N} / \mathrm{c}, l=2 \mathrm{~cm}$ and $a=1 \mathrm{~cm}$ Solution:...
Read More →Show that there can be no net charge in a region in
Question: Show that there can be no net charge in a region in which the electric field is uniform at all points. Solution: Electric field is uniform and given plane is perpendicular to it. Thus it is an equipotential surface with no net current on that surface. So, net charge is: Q = 0...
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Question: Find $\frac{\mathrm{dy}}{\mathrm{dx}}$, when: $y=\frac{(x+1)^{2} \sqrt{x-1}}{(x+4)^{3} \cdot e^{x}}$ Solution:...
Read More →A charge Q is uniformly distributed over a rod of length I.
Question: A charge Q is uniformly distributed over a rod of length I. Consider a hypothetical cube of edge I with the centre of the cube at one end of the rod. Find the minimum possible flux of the electric field through the entire surface of the cube. Solution:...
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Question: Find $\frac{d y}{d x}$, when: $y=\frac{x^{5} \sqrt{x+4}}{(2 x+3)^{2}}$ Solution: Here, we need to take log both the sides to get that differentiation simple....
Read More →The electric field in a region is given by
Question: The electric field in a region is given by $\vec{E}=\frac{3}{5} E_{0} \vec{\imath}+\frac{4}{5} E_{0} \vec{\jmath}$ with $E_{0}=2.0 \times 10^{3} \mathrm{~N} / \mathrm{C}$ Find the flux of this field through a rectangular surface of area $0.2 \mathrm{~m}^{2}$ parallel to the $\mathrm{Y}-\mathrm{Z}$ plane. Solution:...
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Question: Find $\frac{d y}{d x}$, when: $y=\cos x \cos 2 x \cos 3 x$ Solution:...
Read More →Assume that each atom in a copper wire contributes one free electron.
Question: Assume that each atom in a copper wire contributes one free electron. Estimate the number of free electrons in a copper wire having a mass of $6.4 \mathrm{~g}$ (take the atomic weight of copper to be $64 \mathrm{~g} / \mathrm{mol}$ ). Solution:...
Read More →Two particles, carrying -q and +q and having equal masses m each,
Question: Two particles, carrying $-q$ and $+q$ and having equal masses $m$ each, are fixed at the ends of a light rod of length a to forma dipole. The rod is clamped at an end and is placed in a uniform electric field $E$ with the axis of the dipole along the electric field. The rod is slightly tilted and then released. Neglecting gravity find the time period of small oscillations. Solution:...
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Question: Find $\frac{d y}{d x}$, when: $y=(2-x)^{3}(3+2 x)^{5}$ Solution:...
Read More →Find the magnitude of the electric field at the point p
Question: Find the magnitude of the electric field at the point $p$ in the configuration shown in figure (29.E7) for $da$. take $2 q a=p$. Solution:...
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Question: Find $\frac{d y}{d x}$, when: $y=\sqrt{\frac{(x-1)(x-2)}{(x-3)(x-4)(x-5)}}$ Solution:...
Read More →Three charges are arranged on the verticals of an equilateral triangle
Question: Three charges are arranged on the verticals of an equilateral triangle as shown in figure (29.-E6). Find the dipole moment of the combination. Solution:...
Read More →Two particles A and B having opposite charges
Question: Two particles A and B having opposite charges $2.0^{\times 10^{-6}} \mathrm{C}$ and $-2.0^{\times 10^{-6}} \mathrm{C}$, are placed at a separation of $1.0 \mathrm{~cm}$. (a) Write down the electric dipole moment of this pair. (b) Calculate the electric field at a point on the axis of the dipole $1.0 \mathrm{~m}$ away from the centre (c) Calculate the electric field at a point on the perpendicular bisector of the dipole and $1.0 \mathrm{~m}$ away from the centre. Solution:...
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