A narrow beam of singly-charged potassium ions of kinetic energy
Question: A narrow beam of singly-charged potassium ions of kinetic energy $32 \mathrm{keV}$ is injected into a region of width $1.00 \mathrm{~cm}$ having a magnetic field of strength $0.500 T$ as shown in figure. The ions are collected at a screen $95.5 \mathrm{~cm}$ away from the field region. If the beam contains isotopes of atomic weights 39 and 41 , find the separation between the points where these isotopes strike the screen. Take the mass of a potassium ion $=A\left(1.6 \times 10^{-27}\ri...
Read More →Fe+ ions are accelerated through a potential difference of 500V
Question: $\mathrm{Fe}^{+}$ions are accelerated through a potential difference of $500 \mathrm{~V}$ and are injected normally into a homogeneous magnetic field $\mathrm{B}$ of strength $20.0 \mathrm{mT}$. Find the radius of the circular paths followed by the isotopes with mass number 57 and 58 . Take the mass of an ion $=A\left(1.6 \times 10^{-27}\right)_{\mathrm{kg}}$ where $\mathrm{A}$ is the mass number. Solution:...
Read More →Protons having kinetic energy K emerge from an accelerator
Question: Protons having kinetic energy $\mathrm{K}$ emerge from an accelerator as a narrow beam. The beam is bent by a perpendicular magnetic field so that it just misses a plane target kept at a distance $I$ in front of the accelerator. Find the magnetic field. Solution:...
Read More →An electron having a kinetic energy of
Question: An electron having a kinetic energy of $100 \mathrm{eV}$ circulates in a path of radius $10 \mathrm{~cm}$ in a magnetic field. Find the magnetic field and the number of revolutions per second made by the electron. Solution:...
Read More →A proton describes a circle of radius 1cm
Question: A proton describes a circle of radius $1 \mathrm{~cm}$ in a magnetic field of strength $0.10 \mathrm{~T}$. What would be the radius of the circle described by an $\alpha$ - particle moving with the same speed in the same magnetic field? Solution:...
Read More →A particle having a charge
Question: A particle having a charge $2.0 \times 10^{8} \mathrm{C}$ and a mass of $2.0 \times 10^{-10} \mathrm{~g}$ is projected with a speed of $2.0 \times 10^{3} \mathrm{~m} / \mathrm{s}$ in a region having a uniform magnetic field of $0.10 \mathrm{~T}$. The velocity is perpendicular to the field. Find the radius of the circle formed by the particle and also the time period. Solution:...
Read More →Find the point of local maxima or local minima or local minima and the corresponding
Question: Find the point of local maxima or local minima or local minima and the corresponding local maximum and minimum values of each of the following functions: $f(x)=-x^{3}+12 x^{2}-5$ Solution:...
Read More →Find the point of local maxima or local minima or local minima
Question: Find the point of local maxima or local minima or local minima and the corresponding local maximum and minimum values of each of the following functions: $f(x)=x^{4}-62 x^{2}+120 x+9$ Solution:...
Read More →Find the point of local maxima or local minima or local minima and the corresponding
Question: Find the point of local maxima or local minima or local minima and the corresponding local maximum and minimum values of each of the following functions: $f(x)=x^{3}-6 x^{2}+9 x+15$ Solution: $F(1)=19$...
Read More →Find the point of local maxima or local minima or local minima and the corresponding
Question: Find the point of local maxima or local minima or local minima and the corresponding local maximum and minimum values of each of the following functions: $f(x)=2 x^{3}-21 x^{2}+36 x-20$ Solution:...
Read More →Find the point of local maxima or local minima or local minima
Question: Find the point of local maxima or local minima or local minima and the corresponding local maximum and minimum values of each of the following functions: $f(x)=x^{2}$ Solution:...
Read More →Find the point of local maxima or local minima or local minima and the corresponding local
Question: Find the point of local maxima or local minima or local minima and the corresponding local maximum and minimum values of each of the following functions: $f(x)=(x-3)^{4}$ Solution: $\square$ local max. Vaue is $0 .$...
Read More →Find the maximum or minimum values, if any, without using derivatives, of the function:
Question: Find the maximum or minimum values, if any, without using derivatives, of the function: $|\sin 4 x+3|$ Solution:...
Read More →Find the maximum or minimum values, if any, without using derivatives, of the function:
Question: Find the maximum or minimum values, if any, without using derivatives, of the function: $\sin 2 x+5$ Solution:...
Read More →Find the maximum or minimum values, if any, without using derivatives, of the function:
Question: Find the maximum or minimum values, if any, without using derivatives, of the function: $-|x+4|+6$ Solution: It has no minimumvalue as it can have infinitely many....
Read More →Find the maximum or minimum values, if any, without using derivatives, of the function:
Question: Find the maximum or minimum values, if any, without using derivatives, of the function: $-(x-3)^{2}+9$ Solution:...
Read More →Find the maximum or minimum values, if any, without using derivatives, of the function:
Question: Find the maximum or minimum values, if any, without using derivatives, of the function: $(5 x-1)^{2}+4$ Solution:...
Read More →Solve this following
Question: If $f(\mathrm{x})=\mathrm{x}(1-\log \mathrm{x})$, where $\mathrm{c}0$, show that $(\mathrm{a}-\mathrm{b}) \log \mathrm{c}=\mathrm{b}(1-\log \mathrm{b})-\mathrm{a}(1-\log \mathrm{a})$, where $0\mathrm{a}\mathrm{c}$ b. Solution:...
Read More →A current i is passed through a silver strip of width d and width d and area of cross-section A.
Question: A current $i$ is passed through a silver strip of width $d$ and width $d$ and area of cross-section $A$. The number of free electrons per unit volume is $\mathrm{n}$. (a) Find the drift velocity $\mathrm{v}$ of the electrons. (b) If a magnetic field $B$ exists in the region as shown in figure, what is the average magnetic force on the free electrons? (c) Due to the magnetic force, the free electrons get accumulated on one side of the conductor along its length. This produces a transver...
Read More →Find the points on the curve
Question: Find the points on the curve $y=x^{3}-3 x$, where the tangent to the curve is parallel to the chord joining (1, $-2)$ and $(2,2)$. Solution:...
Read More →A conducting wire of length l, lying normal to a magnetic field B,
Question: A conducting wire of length $\mathrm{I}$, lying normal to a magnetic field B, moves a velocity $v$ as shown in figure. (a) Find the average magnetic force on a free electron of the wire. (b) Due to this magnetic force, electrons concentrate at one end resulting in an electric field inside the wire. The redistribution stops when the electric force on the free electrons balances the magnetic force on the free electron balances the magnetic force. Find the electric field developed inside ...
Read More →Find a point on the curve
Question: Find a point on the curve $y=x^{3}$, where the tangent to the curve is parallel to the chord joining the points ( 1 , 1) and $(3,27)$. Solution:...
Read More →The magnetic field existing in a region is given by
Question: The magnetic field existing in a region is given by $\vec{B}=B_{0}\left(1+\frac{x}{l}\right) \vec{k}$ A square loop of edge $I$ and carrying a current $i$, is placed with its edge parallel to the $X-Y$ axes. Find the magnitude of the net magnetic force experienced by the loop. Solution:...
Read More →Using Lagrange's mean-value theorem, find a point on the curve
Question: Using Lagrange's mean-value theorem, find a point on the curve $\mathrm{y}=\mathrm{x}^{2}$, where the tangent is parallel to the line joining the point $(1,1)$ and $(2,4)$ Solution:...
Read More →Suppose that the radius of cross-section of the wire used
Question: Suppose that the radius of cross-section of the wire used in the previous problem is $r$. Find the increase in the radius of the loop if the magnetic field is switched off. The Young's modulus of the material of the wire is $Y$. Solution:...
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