A magnetic dipole of magnetic moment
Question: A magnetic dipole of magnetic moment $1.44 \mathrm{~A}-\mathrm{m}^{2}$ is placed horizontally with the north pole pointing towards north. Find the position of the neutral point if the horizontal component of the earth's magnetic field is $18 \mu T$. Solution:...
Read More →A bar magnet has a length of 8cm.
Question: A bar magnet has a length of $8 \mathrm{~cm}$. The magnetic field at a point at a distance $3 \mathrm{~cm}$ from the center in the broadside-on position is found to be $4 \times 10^{-6} \mathrm{~T}$. Find the pole strength of the magnet. Solution:...
Read More →Show that the magnetic field at a point due to a magnetic dipole is
Question: Show that the magnetic field at a point due to a magnetic dipole is perpendicular to the magnetic axis if the line joining the point with the center of the dipole makes an angle of $\tan ^{-1}(\sqrt{2})$ with the magnetic axis. Solution:...
Read More →A right circular cylinder is inscribed in a cone. Show that the curved surface area of the cylinder
Question: A right circular cylinder is inscribed in a cone. Show that the curved surface area of the cylinder is maximum when the diameter of the cylinder is equal to the radius of the base of the cone. Solution: this means the radius of the cone is twice the radius of the cylinder or equal to diameter of the cylinder....
Read More →The magnetic field at a point,
Question: The magnetic field at a point, $10 \mathrm{~cm}$ away from a magnetic field dipole, is found to be $2.0 \times 10^{-4} \mathrm{~T}$. Find the magnetic moment of the dipole if the point is (a) in end-on position of the dipole and (b) in broadside-on position of the dipole. Solution:...
Read More →Figure shows some of the equipotential surfaces of the magnetic scalar potential.
Question: Figure shows some of the equipotential surfaces of the magnetic scalar potential. Find the magnetic field $B$ at a point in the region. Solution:...
Read More →A uniform magnetic field of
Question: A uniform magnetic field of $0.20 \times 10^{-3} \mathrm{~T}$ exists in the space. Find the change in the magnetic scalar potential as one move through $50 \mathrm{~cm}$ along the field. Solution:...
Read More →Two long bar magnets are placed with their axes coinciding in
Question: Two long bar magnets are placed with their axes coinciding in such a way that the north pole of the first magnet is $2.0 \mathrm{~cm}$ from the south pole of the second. If both the magnets have a pole strength of 10 A-m, find the force exerted by one magnet on the other. Solution:...
Read More →A long bar magnet has a pole strength of 10 A-m.
Question: A long bar magnet has a pole strength of $10 \mathrm{~A}-\mathrm{m}$. Find the magnetic field at a point on the axis of the magnet at a distance of $5 \mathrm{~cm}$ from the north pole of the magnet. Solution:...
Read More →Find the point on the curve
Question: Find the point on the curve $y^{2}=4 x$ which is nearest to the point $(2,-8)$. Solution:...
Read More →Which fraction exceeds its pth power by the greatest number possible?
Question: Which fraction exceeds its pth power by the greatest number possible? Solution:...
Read More →Prove that the volume of the largest cone that can be inscribed in a sphere
Question: Prove that the volume of the largest cone that can be inscribed in a sphere is $\frac{8}{27}$ of the volume of the sphere. Solution:...
Read More →Show that the height of a closed cylinder of given volume and the least surface area is equal to its diameter.
Question: Show that the height of a closed cylinder of given volume and the least surface area is equal to its diameter. Solution:...
Read More →A capacitor of capacitance 100mf is connected to a battery of
Question: A capacitor of capacitance $100^{\mu \mathrm{F}}$ is connected to a battery of $20 v o l t$ for a long time and then disconnected from it. It is now connected across a long solenoid having 4000 turns per meter. It is found that the potential difference across the capacitor drops to $90 \%$ of its maximum value in $2.0$ seconds. Estimate the average the magnetic field produced at the center of the solenoid during this period. Solution:...
Read More →A capacitor of capacitance 100mf is connected to a battery of
Question: A capacitor of capacitance $100^{\mu \mathrm{F}}$ is connected to a battery of $20 v o l t$ for a long time and then disconnected from it. It is now connected across a long solenoid having 4000 turns per meter. It is found that the potential difference across the capacitor drops to $90 \%$ of its maximum value in $2.0$ seconds. Estimate the average the magnetic field produced at the center of the solenoid during this period. Solution:...
Read More →A tightly-wound, long solenoid is kept with its axis parallel to
Question: A tightly-wound, long solenoid is kept with its axis parallel to a large metal sheet carrying a surface current. The surface current through a width dl of the sheet is $\mathrm{Kdl}$ and the number of turns per unit length of the solenoid is $\mathrm{n}$. The magnetic field near the center of the solenoid is found to bero. (a) Find the current in the solenoid. (b) If the solenoid is rotated to make its axis perpendicular to the metal sheet, what would be the magnitude of the magnetic f...
Read More →Find the radius of a closed right circular cylinder of volume
Question: Find the radius of a closed right circular cylinder of volume $100 \mathrm{~cm}^{3}$ which has the minimum total surface area. Solution: Therefore when the total surface area of a cone is minimum, then height of the cone is equal to twice the radius or equal to its diameter....
Read More →A tightly-wound, long solenoid has n turns per unit length,
Question: A tightly-wound, long solenoid has $\mathrm{n}$ turns per unit length, a radius $\mathrm{r}$ and carries a current $\mathrm{i}$. A particle having charge $q$ and mass $m$ is projected from a point on the axis in a direction perpendicular to the axis. What can be the maximum speed for which the particle does not strike the solenoid? Solution:...
Read More →A tightly-wound, long solenoid carries a current of
Question: A tightly-wound, long solenoid carries a current of $2.00 \mathrm{~A}$. An electron is found to execute a uniform circular motion inside the solenoid with a frequency of $1.00 \times 10^{8} \mathrm{rev} / \mathrm{s}$. Find the number of turns per meter in the solenoid. Solution:...
Read More →A tightly-wound solenoid of radius a and length I has n turns per unit length.
Question: A tightly-wound solenoid of radius a and length I has $n$ turns per unit length. It carries an electric current $i$. Consider a length $\mathrm{dx}$ of the solenoid at a distance $x$ from one end. This contains $\mathrm{ndx}$ turns and may be approximated as a circular current i $\mathrm{n} \mathrm{dx}$. (a) Write the magnetic field at the center of the solenoid due to this circular current. Integrate this expression under proper limits to find the magnetic field at the center of the s...
Read More →A copper wire having resistance 0.01ohm
Question: A copper wire having resistance $0.01$ ohm in each meter is used to wind a 400 -turn solenoid of radius $1.0 \mathrm{~cm}$ and length $20 \mathrm{~cm}$. Find the emf of a battery which when connected across the solenoid will cause a magnetic field of $1.0 \times 10^{-2}$ T near the center of the solenoid. Solution:...
Read More →A long solenoid is fabricated by closely winding a wire of radius
Question: A long solenoid is fabricated by closely winding a wire of radius $0.5 \mathrm{~mm}$ over a cylindrical nonmagnetic frame so that the successive turns nearly touch each other. What would be the magnetic field $B$ at the center of the solenoid if it carries a current of $5 \mathrm{~A}$ ? Solution:...
Read More →The magnetic field B inside a long solenoid,
Question: The magnetic field $\mathrm{B}$ inside a long solenoid, carrying a current of $5.00 \mathrm{~A}$, is $3.14 \times 10^{-2} \mathrm{~T}$. Find the number of turns per unit length of the solenoid. Solution:...
Read More →Consider the situation of the previous problem.
Question: Consider the situation of the previous problem. A particle having charge $\mathrm{q}$ and mass $\mathrm{m}$ is projected from the point $Q$ in a direction going into the plane of the diagram. It is found to be describe a circle of radius $r$ between the two plates. Find the speed of the charged particle. Solution:...
Read More →Two large metal sheets carry surface currents as shown in figure.
Question: Two large metal sheets carry surface currents as shown in figure. The current through a strip of width dl is $\mathrm{Kdl}$ where $\mathrm{K}$ is constant. Find the magnetic field at the points $\mathrm{P}, \mathrm{Q}$ and $\mathrm{R}$. Solution:...
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