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13 Electromagnetism I
13.77 Show that Faraday’s law ξ = dϕ B /dt is dimensionally correct.
13.78 The magnetic field of an electromagnetic wave is given by the relation
B = 3 × 10
−12 sin(4 × 10
6 t)
where all quantities are in S.I. units. Find the magnitude of emf induced by
the field in a 200-turn coil of 15 cm 2 area placed normal to the field.
13.79 Find the ratio of emf generated in a loop antenna by 100 MHz (typical television frequency) to that of 1 MHz (typical radio frequency) if both have equal
field intensities.
13.80 Define magnetic flux and state Faraday’s law, describing the relationship
between the magnetic flux linked through a circuit and the current induced in
the circuit. What is the force on a straight wire of length l carrying a current
I in the presence of a magnetic field B?
Two long frictionless and resistanceless parallel rails, separated by a distance
a, are connected by a resistanceless wire. A magnetic field B is oriented
perpendicular to the plane containing the two rails. A frictionless conduction
slider of resistance R and mass m is placed perpendicular to the rails and
is given an initial velocity u along the rails. Obtain an expression for the
force F on the slider while it moves at velocity v. Hence, find the maximum
distance that the slider travels?
13.81 A flat, circular coil has 100 turns of wire, of radius 10 cm. A uniform magnetic field exists in a direction perpendicular to the plane of the coil. This
field is increasing at a rate of 0.1 T/s. Calculate the emf induced in the coil.
13.82 A rectangular coil in the plane of the page has dimensions a and b. A
long wire that carries a current I is placed directly on the coil, as shown
in Fig. 13.20.
(i) Obtain an expression for the magnetic flux through the coil as a function
of x for 0 ≤ x ≤ b.
(ii) For what value of x is the net flux through the coil a maximum? For
what value of x is the net flux a minimum?
Fig. 13.20
13 Electromagnetism I
13.77 Show that Faraday’s law ξ = dϕ B /dt is dimensionally correct.
13.78 The magnetic field of an electromagnetic wave is given by the relation
B = 3 × 10
−12 sin(4 × 10
6 t)
where all quantities are in S.I. units. Find the magnitude of emf induced by
the field in a 200-turn coil of 15 cm 2 area placed normal to the field.
13.79 Find the ratio of emf generated in a loop antenna by 100 MHz (typical television frequency) to that of 1 MHz (typical radio frequency) if both have equal
field intensities.
13.80 Define magnetic flux and state Faraday’s law, describing the relationship
between the magnetic flux linked through a circuit and the current induced in
the circuit. What is the force on a straight wire of length l carrying a current
I in the presence of a magnetic field B?
Two long frictionless and resistanceless parallel rails, separated by a distance
a, are connected by a resistanceless wire. A magnetic field B is oriented
perpendicular to the plane containing the two rails. A frictionless conduction
slider of resistance R and mass m is placed perpendicular to the rails and
is given an initial velocity u along the rails. Obtain an expression for the
force F on the slider while it moves at velocity v. Hence, find the maximum
distance that the slider travels?
13.81 A flat, circular coil has 100 turns of wire, of radius 10 cm. A uniform magnetic field exists in a direction perpendicular to the plane of the coil. This
field is increasing at a rate of 0.1 T/s. Calculate the emf induced in the coil.
13.82 A rectangular coil in the plane of the page has dimensions a and b. A
long wire that carries a current I is placed directly on the coil, as shown
in Fig. 13.20.
(i) Obtain an expression for the magnetic flux through the coil as a function
of x for 0 ≤ x ≤ b.
(ii) For what value of x is the net flux through the coil a maximum? For
what value of x is the net flux a minimum?
Fig. 13.20