Advertisements
Advertisements
प्रश्न
A bicycle is resting on its stand in the east-west direction and the rear wheel is rotated at an angular speed of 100 revolutions per minute. If the length of each spoke is 30.0 cm and the horizontal component of the earth's magnetic field is 2.0 × 10−5 T, find the emf induced between the axis and the outer end of a spoke. Neglect centripetal force acting on the free electrons of the spoke.
उत्तर
Given:-
Length of the spoke of the bicycle's wheel, l = 0.3 m
Earth's magnetic field,
\[\overrightarrow B=2.0\times10^{-5}T\]
Length of each spoke = 30.0 cm = 0.3 m
Angular speed of the wheel,
\[\omega = \frac{100}{60} \times 2\pi = \frac{10}{3}\pi rad/s\]
Linear speed of the spoke,
\[v = \frac{l}{2} \times \omega = \frac{0 . 3}{2} \times \frac{10}{3}\pi\]
Now,
Emf induced in the spoke of the wheel, e = Blv
\[\Rightarrow e = (2 . 0 \times {10}^{- 5} ) \times (0 . 3) \times \left( \frac{0 . 3}{2} \times \frac{10}{3} \times \pi \right)\]
= 3π × 10−6 V
= 3 × 3.14 × 10−6V
= 9.42 × 10−6 V
APPEARS IN
संबंधित प्रश्न
What is motional emf? State any two factors on which it depends.
A rod of length l rotates with a small but uniform angular velocity ω about its perpendicular bisector. A uniform magnetic field B exists parallel to the axis of rotation. The potential difference between the centre of the rod and an end is ______________ .
A small, conducting circular loop is placed inside a long solenoid carrying a current. The plane of the loop contains the axis of the solenoid. If the current in the solenoid is varied, the current induced in the loop is __________________ .
An LR circuit with a battery is connected at t = 0. Which of the following quantities is not zero just after the connection?
A conducting circular loop having a radius of 5.0 cm, is placed perpendicular to a magnetic field of 0.50 T. It is removed from the field in 0.50 s. Find the average emf produced in the loop during this time.
Figure shows a conducting square loop placed parallel to the pole-faces of a ring magnet. The pole-faces have an area of 1 cm2 each and the field between the poles is 0.10 T. The wires making the loop are all outside the magnetic field. If the magnet is removed in 1.0 s, what is the average emf induced in the loop?
A circular coil of radius 2.00 cm has 50 turns. A uniform magnetic field B = 0.200 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 60.0°. The operation takes 0.100 s. (a) Find the average emf induced in the coil. (b) If the coil is a closed one (with the two ends joined together) and has a resistance of 4.00 Ω, calculate the net charge crossing a cross-section of the wire of the coil.
A metallic metre stick moves with a velocity of 2 m s−1 in a direction perpendicular to its length and perpendicular to a uniform magnetic field of magnitude 0.2 T. Find the emf induced between the ends of the stick.
A wire of length 10 cm translates in a direction making an angle of 60° with its length. The plane of motion is perpendicular to a uniform magnetic field of 1.0 T that exists in the space. Find the emf induced between the ends of the rod if the speed of translation is 20 cm s−1.
A rectangular frame of wire abcd has dimensions 32 cm × 8.0 cm and a total resistance of 2.0 Ω. It is pulled out of a magnetic field B = 0.020 T by applying a force of 3.2 × 10−5N (see the following figure). It is found that the frame moves with constant speed. Find (a) this constant speed, (b) the emf induced in the loop, (c) the potential difference between the points aand b and (d) the potential difference between the points c and d.
The current generator Ig' shown in figure, sends a constant current i through the circuit. The wire cd is fixed and ab is made to slide on the smooth, thick rails with a constant velocity v towards right. Each of these wires has resistance r. Find the current through the wire cd.
The magnetic field in a region is given by \[\overrightarrow{B} = \overrightarrow{k} \frac{B_0}{L}y\] where L is a fixed length. A conducting rod of length L lies along the Y-axis between the origin and the point (0, L, 0). If the rod moves with a velocity v = v0 \[\overrightarrow{i},\] find the emf induced between the ends of the rod.
An alternating emf of 110 V is applied to a circuit containing a resistance R of 80 Ω and an inductor L in series. The current is found to lag behind the supply voltage by an angle 8 = tan-1 (3/4). Find the :
(i) Inductive reactance
(ii) Impedance of the circuit
(iii) Current flowing in the circuit
(iv) If the inductor has a coefficient of self-inductance of 0.1 H, what is the frequency of the applied emf?
In the given figure current from A to B in the straight wire is decreasing. The direction of induced current in the loop is A ______.
A conducting square loop of side 'L' and resistance 'R' moves in its plane with the uniform velocity 'v' perpendicular to one of its sides. A magnetic induction 'B' constant in time and space pointing perpendicular and into the plane of the loop exists everywhere as shown in the figure. The current induced in the loop is ______.
A rectangular loop of sides 8 cm and 2 cm with a small cut is stationary in a uniform magnetic field directed normal to the loop. The magnetic field is reduced from its initial value of 0.3 T at the rate of 0.02 T s-1 If the cut is joined and loop has a resistance of 1.6 Ω, then how much power is dissipated by the loop as heat?
