Advertisements
Advertisements
प्रश्न
A rectangular conducting loop consists of two wires on two opposite sides of length l joined together by rods of length d. The wires are each of the same material but with cross-sections differing by a factor of 2. The thicker wire has a resistance R and the rods are of low resistance, which in turn are connected to a constant voltage source V0. The loop is placed in uniform a magnetic field B at 45° to its plane. Find τ, the torque exerted by the magnetic field on the loop about an axis through the centres of rods.
उत्तर
After analyzing the direction of current in both wires, magnetic forces and torques need to be calculated for finding the net torque.
Front view
Side view
According to the problem, the thicker wire has a resistance R, then the other wire has a resistance 2R as the wires are of the same material so their resistivity remains same.
Now, the force and hence, torque on first wire is given by
`F_1 = i_1 lB sin 90^circ = V_circ/(2R) lB`,
`τ_1 = d/(2sqrt(2)) F_1 = (V_0ldB)/(2sqrt(2)R)`
Similarly, the force hence torque on other wire is given by
`F_2 = i_2 lB sin 90^circ = V_circ/(2R) lB`,
`τ_2 = d/(2sqrt(2)) F_2 = (V_0ldB)/(4sqrt(2)R)`
So, net torque, `τ = τ_1 - τ_2`
`τ = 1/(4sqrt(2)) = (V_0AB)/R`
Where A is the area of rectangular coil.
APPEARS IN
संबंधित प्रश्न
A rectangular loop of wire of size 2 cm × 5 cm carries a steady current of 1 A. A straight long wire carrying 4 A current is kept near the loop as shown. If the loop and the wire are coplanar, find (i) the torque acting on the loop and (ii) the magnitude and direction of the force on the loop due to the current carrying wire.
A rectangular loop of size l × b carrying a steady current I is placed in a uniform magnetic field `vecB`. Prove that the torque `vectau`acting on the loop is give by `vectau =vecm xx vecB,`where `vecm` is the magnetic moment of the loop.
A magnetised needle of magnetic moment 4.8 × 10−2 JT−1 is placed at 30° with the direction of uniform magnetic field of magnitude 3 × 10−2 T. Calculate the torque acting on the needle.
The rectangular wire-frame, shown in figure, has a width d, mass m, resistance R and a large length. A uniform magnetic field B exists to the left of the frame. A constant force F starts pushing the frame into the magnetic field at t = 0. (a) Find the acceleration of the frame when its speed has increased to v. (b) Show that after some time the frame will move with a constant velocity till the whole frame enters into the magnetic field. Find this velocity v0. (c) Show that the velocity at time t is given by
v = v0(1 − e−Ft/mv0).
A square loop of side 'a' carrying a current I2 is kept at distance x from an infinitely long straight wire carrying a current I1 as shown in the figure. Obtain the expression for the resultant force acting on the loop.
A planar loop of rectangular shape is moved within the region of a uniform magnetic field acting perpendicular to its plane. What is the direction and magnitude of the current induced in it?
A uniform magnetic field of 3000 G is established along the positive z-direction. A rectangular loop of sides 10 cm and 5 cm carries a current of 12 A. What is the torque on the loop in the different cases shown in fig.? What is the force on each case? Which case corresponds to stable equilibrium?
Consider the motion of a charged particle in a uniform magnetic field directed into the paper. If velocity v of the particle is in the plane of the paper the charged particle will ______.
- Assertion (A): The deflecting torque acting on a current-carrying loop is zero when its plane is perpendicular to the direction of the magnetic field.
- Reason (R): The deflecting torque acting on a loop of the magnetic moment `vecm` in a magnetic field `vecB` is given by the dot product of `vecm` and `vecB`.
