A uniform magnetic field B exists in a cylindrical region of radius 10 cm
Question: A uniform magnetic field $B$ exists in a cylindrical region of radius $10 \mathrm{~cm}$ as shown in figure. A uniform wire of length $80 \mathrm{~cm}$ and resistance $4.0 \Omega$ is bent into a square frame and is placed with one side along a diameter of the cylindrical region. If the magnetic field increases at a constant rate of $0.010 \mathrm{~T} / \mathrm{s}$, find the current induced in the frame. Solution:...
Read More →Find the equations of the tangent and the normal to the given curve at the indicated point for
Question: Find the equations of the tangent and the normal to the given curve at the indicated point for $y=x^{4}-6 x^{3}+13 x^{2}-10 x+5$ at the point where $x=1$ Solution:...
Read More →Find the total heat produced in the loop of the previous problem
Question: Find the total heat produced in the loop of the previous problem during the interval 0 to $30 \mathrm{~s}$ if the resistance of the loop is $4.5 \mathrm{~m} \Omega$. Solution:...
Read More →Find the equations of the tangent and the normal to the given curve at the indicated point for
Question: Find the equations of the tangent and the normal to the given curve at the indicated point for $16 \mathrm{x}^{2}+9 \mathrm{y}^{2}=144$ at $\left(2, \mathrm{y}_{1}\right)$, where $\mathrm{y}_{1}0$ Solution:...
Read More →Find the equations of the tangent and the normal to the given curve at the indicated point for
Question: Find the equations of the tangent and the normal to the given curve at the indicated point for $y=\cot ^{2} x-2 \cot x+2$ at $x=\frac{\pi}{4}$ Solution:...
Read More →Find the equations of the tangent and the normal to the given curve at the indicated point for
Question: Find the equations of the tangent and the normal to the given curve at the indicated point for $\mathrm{y}^{2}=4 \mathrm{ax}$ at $\left(\mathrm{at}^{2}, 2 \mathrm{at}\right)$ Solution:...
Read More →Find the equations of the tangent and the normal to the given curve at the indicated point for
Question: Find the equations of the tangent and the normal to the given curve at the indicated point for $\mathrm{y}=\mathrm{x}^{3}$ at $\mathrm{P}(1,1)$ Solution:...
Read More →Find the equations of the tangent and the normal to the given curve at the indicated point for
Question: Find the equations of the tangent and the normal to the given curve at the indicated point for $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ at $(a \sec \theta, b \tan \theta)$ Solution:...
Read More →Figure shows a square loop of
Question: Figure shows a square loop of $5 \mathrm{~cm}$ being moved towards right at a constant speed of $1 \mathrm{~cm} / \mathrm{s}$. The front edge enters the 20 $\mathrm{cm}$ wide magnetic field at $t=0$. Find the emf induced in the loop at (a) $t=2 s$, (b) $t=10 s$, (c) $t=22 s$ and (d) $t=30 s$. Solution:...
Read More →Find the equations of the tangent and the normal to the given curve at the indicated point for
Question: Find the equations of the tangent and the normal to the given curve at the indicated point for $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ at $(a \cos \theta, b \sin \theta)$ Solution:...
Read More →A wire-loop confined in a plane is rotated in its own plane
Question: A wire-loop confined in a plane is rotated in its own plane with some angular velocity. A uniform magnetic field exists in the region. Find the emf induced in the loop. Solution: No flux change occurs. So emf induced is zero....
Read More →Find the equations of the tangent and the normal to the given curve at the indicated point for
Question: Find the equations of the tangent and the normal to the given curve at the indicated point for $y^{2}=4 a x$ at $\left(\frac{a}{m^{2}}, \frac{2 a}{m}\right)$ Solution:...
Read More →The north pole of a magnet is brought down along the axis of a horizontal circular coil.
Question: The north pole of a magnet is brought down along the axis of a horizontal circular coil. As a result, the flux through the coil changes from $0.35$ weber to $0.85$ weber in an interval of half a second. Find the average emf induced during this period. Is the induced current clockwise or anticlockwise as you look into the coil from the side of the magnet? Solution:...
Read More →A 20 cm long conducting rod is set into pure translation with a uniform velocity of
Question: A $20 \mathrm{~cm}$ long conducting rod is set into pure translation with a uniform velocity of $10 \mathrm{~cm} / \mathrm{s}$ perpendicular to its length. A uniform magnetic field of magnitude $0.10 \mathrm{~T}$ exists in a direction perpendicular to the plane of motion. (a) Find the average magnetic force on the free electrons of the rod. (b)For what electric field inside the rod, the electric force on a free electron will balance the magnetic force? How is the electric field created...
Read More →Find the equations of the tangent and the normal to the given curve at the indicated point for
Question: Find the equations of the tangent and the normal to the given curve at the indicated point for $y=x^{3}-2 x+7$ at $(1,6)$ Solution:...
Read More →A circular coil of one turn of radius
Question: A circular coil of one turn of radius $5.0 \mathrm{~cm}$ is rotated about a diameter with a constant angular speed of 80 revolutions per minute. A uniform magnetic field $B=0.010 \mathrm{~T}$ exists in a direction perpendicular at the axis of rotation. Find (a) the maximum emf induced by the average emf induced in the coil over a long period and (b) the average of the squares of emf induced over a long period. Solution:...
Read More →Find the slope of the tangent to the curve
Question: Find the slope of the tangent to the curve i. $y=\left(x^{3}-x\right)$ at $x=2$ ii. $y=\left(2 x^{2}+3 \sin x\right)$ at $x=0$ iii. $\mathrm{y}=(\sin 2 \mathrm{x}+\cot \mathrm{x}+2)^{2}$ at $\mathrm{x}=\frac{\pi}{2}$ Solution:...
Read More →A coil of radius 10 cm and resistance 40Ω has 1000 turns.
Question: A coil of radius $10 \mathrm{~cm}$ and resistance $40 \Omega$ has 1000 turns. It is placed with its plane vertical and its axis parallel to the magnetic meridian. The coil connected to a galvanometer and is rotated about the vertical diameter through an angle of $180^{\circ}$. Find the charge flows through the galvanometer if the horizontal component of the earth's magnetic field is $B_{H}=3.0 \times 10^{5} \mathrm{~T}$. 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. $f(x)=\frac{3}{10} x^{4}-\frac{4}{5} x^{3}-3 x^{2}+\frac{36}{5} x+11$ Solution:...
Read More →A closed coil having 100 turns is rotated in a uniform magnetic field
Question: A closed coil having 100 turns is rotated in a uniform magnetic field $B=4.0 \times 10^{-4} \mathrm{~T}$ about a diameter which is perpendicular to the field. The angular velocity of rotation is 300 revolutions per minute. The area of the coil is $25 \mathrm{~cm}^{2}$ and its resistance is $4.0 \Omega$. Find (a) the average emf developed in half a turn from a position where the coil is perpendicular to me magnetic field. (b) The average emf in a full turn and (c) the net charge displac...
Read More →A circular coil of radius 2.00 cm and 50 turns.
Question: A circular coil of radius $2.00 \mathrm{~cm}$ and 50 turns. A uniform magnetic field $B=0.200 \mathrm{~T}$ exists in the space in a direction parallel to the axis of the loop. The coil is now rotated about a diameter through an angle of $60^{\circ}$. The operation takes $0.100 \mathrm{~s}$. (a) Find the average emf induced in the coil. (b) If the coil is closed one (with the two ends joined together) and has a resistance of $4.00 \Omega$, calculate the net crossing a cross-section of t...
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. $f(x)=3 x^{4}-4 x^{3}-12 x^{2}+5$ Solution:...
Read More →Figure shows a metallic square frame of edge a in a vertical plane.
Question: Figure shows a metallic square frame of edge a in a vertical plane. A uniform magnetic field B exists in the space in a direction perpendicular to the plane of the figure. Two boys pull the opposite corners of the square to deform it into a rhombus. They start pulling the corners at $\mathrm{t}=0$ and displace the corners at a uniform speed $u$. (a) Find the induced emf in the frame at the instant when the angles at these corners reduce to $60^{\circ}$. (b) Find the induced current in ...
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. $f(x)=x^{4}-8 x^{3}+22 x^{2}-24 x+21$ Solution:...
Read More →A long solenoid of radius 2 cm has 100 turns/cm
Question: A long solenoid of radius $2 \mathrm{~cm}$ has 100 turns/cm and carries a current of $5 \mathrm{~A}$. A coil of radius $1 \mathrm{~cm}$ having 100 turns and a total resistance of $20 \Omega$ is placed inside the solenoid coaxially. The coil is connected to a galvanometer. If the current in the solenoid is reversed in direction, find the charge flown through the galvanometer. Solution:...
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