Sometimes we show an idealized magnetic field
Question: Sometimes we show an idealized magnetic field which is uniform in a given region and falls to zero abruptly. One such field is represented in figure. Using Ampere's law over the path PQRS, show that such a field is not possible. Solution:...
Read More →A solid wire of radius 10cm carries a current of 5.0A
Question: A solid wire of radius $10 \mathrm{~cm}$ carries a current of $5.0 \mathrm{~A}$ distributed uniformly over its cross-section. Find the magnetic field $B$ at a point at a distance (a) $2 \mathrm{~cm}$ (b) $10 \mathrm{~cm}$ and (c) $20 \mathrm{~cm}$ away from the axis. Sketch a graph of $B$ versus $x$ for $0x20 \mathrm{~cm}$. Solution:...
Read More →Show that the right circular cone of the least curved surface and given
Question: Show that the right circular cone of the least curved surface and given volume has an altitude equal to $\sqrt{2}$ times the radius of the base. Solution:...
Read More →A long, cylindrical wire of radius b carries a current i distributed over its cross-section.
Question: A long, cylindrical wire of radius b carries a current i distributed over its cross-section. Find the magnitude of the magnetic field at a point inside the wire at a distance a from the axis. Solution:...
Read More →A long, cylindrical tube of inner and outer radii a and b
Question: A long, cylindrical tube of inner and outer radii a and b carries a current i distributed uniformly over its cross-section. Find the magnitude of the magnetic field at a point (a) just inside the tube. (b) Just outside the tube. Solution:...
Read More →A thin but long, hollow, cylindrical tube of radius r carries
Question: A thin but long, hollow, cylindrical tube of radius r carries a current $i$ along its length. Find the magnitude of the magnetic field at a distance $r / 2$ from the surface (a) inside the tube. (b) Outside the tube. Solution:...
Read More →A charge of
Question: A charge of $3.14 \times 10^{-6} \mathrm{C}$ is distributed uniformly over a circular ring of radius $20.0 \mathrm{~cm}$. The ring rotates about its axis with an angular velocity of $60.0 \mathrm{rad} / \mathrm{s}$. Find the ratio of the electric field to the magnetic field at a point on the axis at a distance of $5.00 \mathrm{~cm}$ from the center. Solution:...
Read More →A cylindrical can is to be made to hold 1 litre of oil.
Question: A cylindrical can is to be made to hold 1 litre of oil. Find the dimensions which will minimize the cost of the metal to make the can. Solution:...
Read More →A circular loop of radius 4.0cm is placed in a horizontal
Question: A circular loop of radius $4.0 \mathrm{~cm}$ is placed in a horizontal plane and carries an electric current of $5.0 \mathrm{~A}$ in the clockwise direction as seen from above. Find the magnetic field (a) at a point $3.0 \mathrm{~cm}$ above the center of the loop. (b) At a point $3.0 \mathrm{~cm}$ below the center of the loop. Solution:...
Read More →A circular coil of 200 turns has a radius of
Question: A circular coil of 200 turns has a radius of $10 \mathrm{~cm}$ and carries a current of $2.0 \mathrm{~A}$. (a) Find the magnitude of the magnetic field $\overrightarrow{\mathrm{B}}$ at the center of the coil. (b) At what distance from the center along the axis of the coil will the field B drop to half its value at the center? ( $\sqrt{4}=1.5874 \ldots .)$ Solution:...
Read More →A circular loop of radius r carries a current i.
Question: A circular loop of radius $r$ carries a current i. How should a long, straight wire carrying a current $4 \mathrm{i}$ be placed in the plane of the circle so that the magnetic field at the center becomes zero? Solution:...
Read More →A piece of wire carrying a current of 6.00A
Question: A piece of wire carrying a current of $6.00 \mathrm{~A}$ is bent in the form of a circular arc of radius $10.0 \mathrm{~cm}$, and it subtends an angle of $120^{\circ}$ at the center. Find the magnetic field B due to this piece of wire at the center. Solution:...
Read More →An open box with a square base is to be made out of a given cardboard
Question: An open box with a square base is to be made out of a given cardboard of area $\mathrm{c}^{2}$ (square) units. Show that the maximum volume of the box is $\frac{\mathrm{c}^{3}}{6 \sqrt{3}}$ (cubic) units. Solution:...
Read More →Find the magnetic field B due to a semicircular wire of radius
Question: Find the magnetic field B due to a semicircular wire of radius $10.0 \mathrm{~cm}$ carrying a current of $5.0 \mathrm{~A}$ as its center of curvature. Solution:...
Read More →A circular loop of radius r carrying a current i is held
Question: A circular loop of radius $r$ carrying a current $i$ is held at the center of another circular loop of radius $R$ ( $r$ ) carrying a current I. The plane of the smaller loop makes an angle of $30^{\circ}$ with that of the larger loop. If the smaller loop is held fixed in this position by applying a single force at a point on its periphery, what would be the minimum magnitude of this force? Solution:...
Read More →A circular loop of radius R carries a current I.
Question: A circular loop of radius $R$ carries a current $I$. Another circular loop of radius $r(\llR)$ carries a current i and is placed at the center of the larger loop. The planes of the two circles are at right angle to each other. Find the torque acting on the smaller loop. Solution:...
Read More →A circular loop of radius 20cm carries a current of 10A.
Question: A circular loop of radius $20 \mathrm{~cm}$ carries a current of $10 \mathrm{~A}$. An electron crosses the plane of the loop with a speed of $2.0 \times 10^{6} \mathrm{~m} / \mathrm{s}$. The direction of motion makes an angle of $30^{\circ}$ with the axis of the circle and passes through its center. Find the magnitude of the magnetic force on the electron at the instant it crosses the plane. Solution:...
Read More →A square piece of tin of side
Question: A square piece of tin of side $12 \mathrm{~cm}$ is to be made into a box without a lid by cutting a square from each corner and folding up the flaps to form the sides. What should be the side of the square to be cut off so that the volume of the box is maximum? Also, find this maximum volume. Solution:...
Read More →If the outer coil of the previous problem is rotated through
Question: If the outer coil of the previous problem is rotated through $90^{\circ}$ about a diameter, what would be the magnitude of the magnetic field B at the center? Solution:...
Read More →Two circular coils of radii 5.0cm and 10cm carry equal currents of 2.0A.
Question: Two circular coils of radii $5.0 \mathrm{~cm}$ and $10 \mathrm{~cm}$ carry equal currents of $2.0 \mathrm{~A}$. The coils have 50 and 100 turns respectively and are placed in such a way that their planes as well as the centers coincide. Find the magnitude of the magnetic field B at the common center of the coils if the currents in the coils are (a) in the same sense. (b) in the opposite sense. Solution:...
Read More →A current-carrying circular coil of 100 turns and radius
Question: A current-carrying circular coil of 100 turns and radius $5.0 \mathrm{~cm}$ produces a magnetic field of $6.0 \times 10^{-5} \mathrm{~T}$ at its center. Find the value of the current. Solution:...
Read More →A circular loop of one turn carries a current of 5.00A.
Question: A circular loop of one turn carries a current of $5.00 \mathrm{~A}$. If the magnetic field $\mathrm{B}$ at the center is $0.200 \mathrm{mT}$, find the radius of the loop. Solution:...
Read More →A square loop PQRS carrying a current of 6.0A
Question: A square loop PQRS carrying a current of $6.0 \mathrm{~A}$ is placed near a long wire carrying $10 \mathrm{~A}$ as shown in figure. (a) Show that the magnetic force acting on the part $P Q$ is equal and opposite to that on the part Rs. (b) Find the magnetic force on the square loop. Solution:...
Read More →A long, straight wire is fixed horizontally and carries a current of
Question: A long, straight wire is fixed horizontally and carries a current of $50.0 \mathrm{~A}$. A second wire having linear mass density $1.0 \times 10^{-4} \mathrm{~kg} / \mathrm{m}$ is placed parallel to and directly above this wire at a separation of $5.0 \mathrm{~mm}$. What current should this second wire carry such that the magnetic repulsion can balance its weight? Solution:...
Read More →A window is in the form of a rectangle surmounted by a semicircular opening
Question: A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 metres. Find the dimensions of the windows to admit maximum light through it. Solution:...
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