Find the intervals on which each of the following functions is
Question: Find the intervals on which each of the following functions is (a) increasing (b) decreasing. $f(x)=2 x^{3}+9 x^{2}+12 x+15$ Solution:...
Read More →A conducting loop of face-area A and resistance
Question: A conducting loop of face-area A and resistance $\mathrm{R}$ is placed perpendicular to a magnetic field B. The loop is withdrawn completely from the field. Find the charge which flows through any cross-section of the wire in the process. Note that it independent of the shape of the loop as well as the way it is withdrawn. Solution:...
Read More →A conducting square loop having edges of length
Question: A conducting square loop having edges of length $2.0 \mathrm{~cm}$ is rotated through $180^{\circ}$ about a diagonal in $0.20 \mathrm{~s}$. A magnetic field B exists in the region which is perpendicular to the loop in its initial position. If the average induced emf during the rotation is $20 \mathrm{mv}$, find the magnitude of the magnetic field. Solution:...
Read More →Find the intervals on which each of the following functions is
Question: Find the intervals on which each of the following functions is (a) increasing (b) decreasing. $f(x)=\left(x^{4}-4 x^{3}+4 x^{2}+15\right)$ Solution:...
Read More →The given figure shows a conducting square loop placed parallel
Question: The given figure shows a conducting square loop placed parallel to the pole-faces of a ring magnet. The pole-faces have an area of $1 \mathrm{~cm}^{2}$ each and the field between the poles is $0.10 \mathrm{~T}$. The wires making the loop are all outside the magnetic field. If the magnet is removed in $1.0 \mathrm{~s}$. What is the average emf induced in the loop? Solution:...
Read More →A conducting loop of area
Question: A conducting loop of area $5.0 \mathrm{~cm}^{2}$ is placed in a magnetic field which varies sinusoidally with time as $B=B_{v}$ sin $\omega t$ where $B_{v}=0.20 \mathrm{~T}$ and $\omega=300 \mathrm{~s}^{-1}$. The normal to the coil makes an angle of $60^{\circ}$ with the field. Find (a) The maximum emf induced in the coil, (b) the emf induced at $r=(\pi / 900) s$ and (c) the emf induced at $t=\left(\frac{\pi}{600}\right) s$ Solution:...
Read More →Find the intervals on which each of the following functions is
Question: Find the intervals on which each of the following functions is (a) increasing (b) decreasing. $f(\mathrm{x})=(\mathrm{x}-1)(\mathrm{x}-2)^{2}$ Solution:...
Read More →Suppose the resistance of the coil in the previous problem is
Question: Suppose the resistance of the coil in the previous problem is $25 \Omega$. Assume that the coil moves with uniform velocity during its removal and restoration. Find the thermal energy developed in the coil during (a) its removal (b) its restoration (c) its motion Solution:...
Read More →Find the intervals on which each of the following functions is
Question: Find the intervals on which each of the following functions is (a) increasing (b) decreasing. $f(x)=2 x^{3}-24 x+5$ Solution:...
Read More →A square shaped copper coil has edges of
Question: A square shaped copper coil has edges of length $50 \mathrm{~cm}$ and contains 50 turns. It is placed perpendicular to a $1.0 T$ magnetic field. It is removed from the magnetic field in $0.25 \mathrm{~s}$ and restored in its original place in the next $0.25 \mathrm{~s}$. Find the magnitude of average emf induced in the loop during (a) its removal. (b) Its restoration. (c) Its motion. Solution:...
Read More →A conducting circular loop of area
Question: A conducting circular loop of area $1 \mathrm{~mm}^{2}$ is placed coplanarly with a long, straight wire at a distance of $20 \mathrm{~cm}$ from it. The straight wire carries an electric current which changes from $10 \mathrm{~A}$ to zero in $0.1 \mathrm{~s}$. Find the average emf induced in the loop in $0.1 \mathrm{~s}$ Solution:...
Read More →Solve this following
Question: Find the intervals on which each of the following functions is (a) increasing (b) decreasing. $f(x)=\left(6+12 x+3 x^{2}-2 x^{3}\right)$ Solution:...
Read More →Find the intervals on which each of the following functions is
Question: Find the intervals on which each of the following functions is $(a)$ increasing $(b)$ decreasing. $f(x)=\left(x^{3}-6 x^{2}+9 x+10\right)$ Solution:...
Read More →Find the intervals on which each of the following functions is
Question: Find the intervals on which each of the following functions is (a) increasing (b) decreasing. $f(x)=x^{3}-12 x^{2}+36 x+17$ Solution:...
Read More →A conducting circular loop having a radius
Question: A conducting circular loop having a radius $5.0 \mathrm{~cm}$, is placed perpendicular to a magnetic field of $0.50 \mathrm{~T}$. It is removed from the field of $0.50 \mathrm{~s}$. Find the average emf produced in the loop during this time. Solution:...
Read More →(a) The magnetic field in a region varies as shown in the given figure.
Question: (a) The magnetic field in a region varies as shown in the given figure. Calculate the average induced emf in a conducting loop of area $2.0 \times 10^{-3} \mathrm{~m}^{2}$ placed perpendicular to the field in each of the $10 \mathrm{~ms}$ intervals shown. (b) In which intervals is the emf not constant? Neglect the behaviour near the ends of $10 \mathrm{~ms}$ intervals. Solution:...
Read More →Find the intervals on which each of the following functions is
Question: Find the intervals on which each of the following functions is (a) increasing (b) decreasing. $f(x)=\left(x^{4}-\frac{x^{3}}{3}\right)$ Solution:...
Read More →The flux of magnetic field through a closed conducting loop changes
Question: The flux of magnetic field through a closed conducting loop changes with time according to the equation, $\phi=a t^{2}+b t+c$ a) Write the SI units of $a, b$ and $c$. b) If the magnitude of $a, b$ and $c$ are $0.20,0.40$ and $0.60$ respectively, find the induced emf at $\mathrm{t}=2 \mathrm{~s}$ Solution:...
Read More →Solve this following
Question: Find the intervals on which the function $f(x)=6-9 x-x^{2}$ is (a) strictly increasing (b) strictly decreasing. Solution:...
Read More →Calculate the dimensions of
Question: Calculate the dimensions of (a) $\int \vec{E} \cdot \overrightarrow{d l}$ (b) $v B l$ and (c) $\frac{d \varphi_{S}}{d t}$ The symbols have their usual meanings Solution:...
Read More →Solve this following
Question: Find the intervals on which the function $f(\mathrm{x})=2 \mathrm{x}^{3}-3 \mathrm{x}^{2}-36 \mathrm{x}+7$ is (a) strictly increasing (b) strictly decreasing. Solution: $F^{\prime}(x)0$ for $x \in(-2,3)$ hence in this interval function is decreasing....
Read More →The coercive force for a certain permanent magnet is
Question: The coercive force for a certain permanent magnet is $4.0 \times 10^{4} \mathrm{~A} \mathrm{~m}^{-1}$. This magnet is placed inside a long solenoid of 40 turns/cm and a current is passed in the solenoid to demagnetise it completely. Find the current. Solution:...
Read More →Solve this following
Question: Find the intervals on which the function $f(x)=\left(2 x^{2}-3 x\right)$ is (a) strictly increasing (b) strictly decreasing. Solution:...
Read More →Assume that each iron atom has a permanent magnetic moment equal to
Question: Assume that each iron atom has a permanent magnetic moment equal to 2 Bohr magnetons (1 Bohr magneton equals $9.27$ $\times 10^{-24} \mathrm{~A} \mathrm{~m}^{2}$ ). The density of atoms in iron is $8.52 \times 10^{28}$ atoms $\mathrm{m}^{-3}$. (a) Find the maximum magnetisation $/$ in a long cylinder of iron (b) Find the maximum magnetic field $B$ on the axis inside the cylinder. Solution: Given that in problem, No of atoms per unit volume is $f=8.52 \times 10^{28}$ atoms $/ \mathrm{m}...
Read More →Solve this following
Question: Show that $f(\mathrm{x})=\frac{(\mathrm{x}-2)}{(\mathrm{x}+1)}$ is increasing for all $\mathrm{x} \in \mathrm{R}$, except at $\mathrm{x}=-1$ Solution:...
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