Advertisements
Advertisements
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.
Advertisements
उत्तर
(1) `vectau=vecM xx vecB = MBsintheta`
Here M and B have the same direction
θ = 0
`|vectau| = MBsintheta =0`
`(2) \text{We know } vecF_B = ivecl xx vecB`
On line AB, and CD magnetic forces are equal and opposite. So they cancel out each other. Magnetic force on line AD.
`vecF = ivecl xx vecB` (Attractive)
=ilB [l =5 cm =0.05 cm]
`because B= (mu_0I)/(2pir)`
`|vecF| = (uiIl)/(2pir)` (Attractive)
Magnetic force on line CB.
`vecF = ivecl xx vecB` [Repulsive]
`=>F' = |vecF'| =ilB'`
`because B' =(mu_0I)/(2pir')`
`F' = (mu_0iIl)/(2pir')` [repulsive]
So, net force
`F_n = F-F'`
`=(mu_0iIl)/(2pi) [1/r - 1/r']`
Given I = 4A
I = 1 A
R = 1 cm = 0.01 m
r′ = (1 + 2) cm = 0.03 m
l = 5 cm = 0.05 m
Plugging in the values
`F = 2 xx 10^-7 (4) (1)(0.05)[1/(0.01) - 1/(0.03)]`
`= 8 xx 10^-7 xx 5 [1/1 - 1/3]`
`= 40 xx 10^-7 [2/3]`
`= 26.66 xx 10^-7`
APPEARS IN
संबंधित प्रश्न
In a chamber, a uniform magnetic field of 6.5 G (1 G = 10–4 T) is maintained. An electron is shot into the field with a speed of 4.8 × 106 m s−1 normal to the field. Explain why the path of the electron is a circle. Determine the radius of the circular orbit. (e = 1.5 × 10–19 C, me = 9.1 × 10–31 kg)
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).
Figure shows a square loop of edge a made of a uniform wire. A current i enters the loop at the point A and leaves it at the point C. Find the magnetic field at the point P which is on the perpendicular bisector of AB at a distance a/4 from it.
Find the magnetic field B at the centre of a rectangular loop of length l and width b, carrying a current i.
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?
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.
