Advertisements
Advertisements
प्रश्न
Find the current in the sliding rod AB (resistance = R) for the arrangement shown in figure. B is constant and is out of the paper. Parallel wires have no resistance. v is constant. Switch S is closed at time t = 0.
Advertisements
उत्तर
This is a similar problem as we discussed above. Here, a conductor of length d moves with speed v, perpendicular to magnetic field B as shown in figure.
Due to this, an motional emf is induced across two ends of rod (e = vBd).
Since, switch S is closed at time t = 0 current starts growing in the inductor by the potential difference due to motional emf.
By applying KVL in the given circuit, we have
`- L (dI)/(dt) + vBd = IR` or `L (dI)/(dt) + IR = vBd`
This is the linear differential equation.
On solving, we get
`I = (vBd)/R + Ae^((- Rt)/2)`
At t = 0, I = 0
⇒ `A = - (vBd)/R`
⇒ `I = (vBd)/R (1 - e^((- Rt)/L))`
This is the required expression of current.
APPEARS IN
संबंधित प्रश्न
Figure shows a straight, long wire carrying a current i and a rod of length l coplanar with the wire and perpendicular to it. The rod moves with a constant velocity v in a direction parallel to the wire. The distance of the wire from the centre of the rod is x. Find the motional emf induced in the rod.
An aircraft of wing span of 50 m flies horizontally in the Earth's magnetic field of 6 x 10-5 T at a speed of 400 m/s. Calculate the emf generated between the tips of the wings of the aircraft.
A cycle wheel of radius 0.6 m is rotated with constant angular velocity of 15 rad/s in a region of magnetic field of 0.2 T which is perpendicular to the plane of the wheel. The e.m.f generated between its center and the rim is, ____________.
A straight conductor of length 2 m moves in a uniform magnetic field of induction 2.5 x `10^-3` T with a velocity. of 4 m/s in a direction perpendicular to its length and also perpendicular to the field. The e.m.f. induced between the ends of the conductor is ______.
A wire of length 50 cm moves with a velocity of 300 m/min, perpendicular to a magnetic field. If the e.m.f. induced in the wire is 2 V, the magnitude of the field in tesla is ______.
The emf induced across the ends of a conductor due to its motion in a magnetic field is called motional emf. It is produced due to magnetic Lorentz force acting on the free electrons of the conductor. For a circuit shown in the figure, if a conductor of length l moves with velocity v in a magnetic field B perpendicular to both its length and the direction of the magnetic field, then all the induced parameters are possible in the circuit.
A conducting rod of length l is moving in a transverse magnetic field of strength B with velocity v. The resistance of the rod is R. The current in the rod is ______.
The emf induced across the ends of a conductor due to its motion in a magnetic field is called motional emf. It is produced due to magnetic Lorentz force acting on the free electrons of the conductor. For a circuit shown in the figure, if a conductor of length l moves with velocity v in a magnetic field B perpendicular to both its length and the direction of the magnetic field, then all the induced parameters are possible in the circuit.
A 0.1 m long conductor carrying a current of 50 A is held perpendicular to a magnetic field of 1.25 mT. The mechanical power required to move the conductor with a speed of 1 ms-1 is ______.
The emf induced across the ends of a conductor due to its motion in a magnetic field is called motional emf. It is produced due to magnetic Lorentz force acting on the free electrons of the conductor. For a circuit shown in the figure, if a conductor of length l moves with velocity v in a magnetic field B perpendicular to both its length and the direction of the magnetic field, then all the induced parameters are possible in the circuit.
A bicycle generator creates 1.5 V at 15 km/hr. The EMF generated at 10 km/hr is ______.
Motional e.m.f is the induced e.m.f. ______
A rod of mass m and resistance R slides smoothly over two parallel perfectly conducting wires kept sloping at an angle θ with respect to the horizontal (Figure). The circuit is closed through a perfect conductor at the top. There is a constant magnetic field B along the vertical direction. If the rod is initially at rest, find the velocity of the rod as a function of time.
An aeroplane, with its wings spread 10 m, is flying at a speed of 180 km/h in a horizontal direction. The total intensity of earth's field at that part is 2.5 × 10-4 Wb/m2 and the angle of dip is 60°. The emf induced between the tips of the plane wings will be ______.
Derive an expression for the total emf induced in a conducting rotating rod.
An aircraft of wing span of 60 m flies horizontally in earth’s magnetic field of 6 × 10−5 T at a speed of 500 m/s. Calculate the e.m.f. induced between the tips of the wings of the aircraft.
A wire of length 1 m moving with velocity 8 m/s at right angles to a magnetic field of 2 T. The magnitude of induced emf, between the ends of wire will be ______.
Figure shows a rectangular frame situated in a constant magnetic field. A wire BC of length 1 m is moved out with velocity 4 m/s. Magnetic field strength is 0.15 T. Force acting on the wire BC is:
