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The magnetic field inside a tightly wound, long solenoid is B = μ0ni. It suggests that the field does not depend on the total length of the solenoid, and hence if we add more loops at the ends of a solenoid the field should not increase. Explain qualitatively why the extra-added loops do not have a considerable effect on the field inside the solenoid.
Consider a long, straight wire of cross-sectional area A carrying a current i. Let there be n free electrons per unit volume. An observer places himself on a trolley moving in the direction opposite to the current with a speed and separated from the wire by a distance r. The magnetic field seen by the observer is very nearly.
A long, straight wire carrying a current of 1.0 A is placed horizontally in a uniform magnetic field B = 1.0 × 10–8 T pointing vertically upward figure. Find the magnitude of the resultant magnetic field at the points P and Q, both situated at a distance of 2.0 cm from the wire in the same horizontal plane.
A long, straight wire of radius r carries a current i and is placed horizontally in a uniform magnetic field B pointing vertically upward. The current is uniformly distributed over its cross section.
(a) At what points will the resultant magnetic field have maximum magnitude?
(b) What will be the minimum magnitude of the resultant magnetic field?
Four long, straight wires, each carrying a current of 5.0 A, are placed in a plane as shown in figure. The points of intersection from a square of side 5.0 cm.
(a) Find the magnetic field at the centre P of the square
(b) Q1, Q2, Q3 and Q4 are points situated on the diagonal of the square and at a distance from P that to equal to the length of the diagonal of the square. Find the magnetic fields at these points.
A long, straight wire carries a current i. Let B1 be the magnetic field at a point P at a distance d from the wire. Consider a section of length ℓ of this wire such that the point P lies on the perpendicular bisector of the section. Let B2 be the magnetic field at this point due to this section only. Find the value of d/ℓ so that B2 differs from B1 by 1%.
A polygon of n equal sides is formed by bending a current carrying wire to total length 2πr which carries a current i.
(a) Find the magnetic field B at the center of the n-sided polygon.
(b) By letting n → ∞, derive the expression for the induced magnetic field at the center of a circular current carrying wire.
Figure shows a part of an electric circuit. The wires AB, CD and EF are long and have identical resistances. The separation between the neighboring wires is 1.0 cm. The wires AE and BF have negligible resistance and the ammeter reads 30 A. Calculate the magnetic force per unit length of AB and CD.
A long, straight wire is fixed horizontally and carries a current of 50.0 A. A second wire having linear mass density 1.0 × 10–4 kg m–1 is placed parallel to and directly above this wire at a separation of 5.0 mm. What current should this second wire carry such that the magnetic repulsion can balance its weight?
. A square loop PQRS carrying a current of 6.0 A is placed near a long wire carrying 10 A as shown in the figure.
(a) Show that the magnetic force acting on the part PQ is equal and opposite to that on the part Rs.
(b) Find the magnetic force on the square loop.
Two circular coils of radii 5.0 cm and 10 cm carry equal currents of 2.0 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 centre of the coils if the currents in the coils are (a) in the same sense (b) in the opposite sense.
A circular loop of radius 20 cm carries a current of 10 A. An electron crosses the plane of the loop with a speed of 2.0 × 106 m s–1. The direction of motion makes an angle of 30° with the axis of the circle and passes through its center. Find the magnitude of the passes through its center. Find the magnitude of the magnetic force on the electron at the instant it crosses the plane.
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 and angle of 30° 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 the force?
A circular coil of 200 turns has a radius of 10 cm and carries a current of 2.0 A.
(a) Find the magnitude of the magnetic field vector 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?
(3√4 = 1.5874)
A tightly-wound solenoid of radius a and length l has n turns per unit length. It carries an electric current i. Consider a length dx of the solenoid at a distance x from one end. This contains n dx turns and may be approximated as a circular current i n 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 solenoid.
(b) Verify that if l >> a, the field tends to B = μ0ni and if a >> l, the field tends to
B=. Interpret these results
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 Kdl and the number of turns per unit length of the solenoid is n. The magnetic field near the center of the solenoid is found to be zero.
(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 field near its center?
A capacitor of capacitance 100 μF is connected to a battery of 20 volts 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 magnetic field produced at the center of the solenoid during this period.