Advertisements
Advertisements
प्रश्न
A rectangular loop of wire of size 4 cm × 10 cm carries a steady current of 2 A. A straight long wire carrying 5 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 vec B = MBsintheta`
Here M and B have the same direction
θ = 0°
`|vectau| = MB sintheta = 0`
(2) 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 [(I = 10cm),(= 0.1cm):]
`because B =( mu_0I)/(2pir)`
`|vecF| = (mui Il)/(2pir)` (Attractive)
Magnetic force on line CB.
`vecF - ivecl xx vecB` [Repulsive]
`=> F= |vecF| = il B'`
`because B' = (mu_0I)/(2pir')`
` F = (mu_0iIl)/(2pir') ` (Repulsive)
So, net force
`F_n = F - F'`
`= (mu_0iIl)/(2pir) [1/r -1/(r')]`
Given i = 5A
I = 2 A
r = 1 cm = 0.01 m
r′ = (1 + 4) cm = 5 cm
= 0.05 m
l = 10 cm = 0.1 m
Plugging in the values in above equation
`F_n = (2 xx 10^-7) (5)(2)(0.1)[1/0.01 - 1/0.05]`
`= 2 xx 10 xx 10^-7 xx 10 [1/1 - 1/5]`
` = 200 xx 10^-7 [(5-1)/5]`
`= 200 xx 10^-7 xx 4/5`
`=160 xx 10^-7 N`
APPEARS IN
संबंधित प्रश्न
A square coil of side 10 cm consists of 20 turns and carries a current of 12 A. The coil is suspended vertically and the normal to the plane of the coil makes an angle of 30° with the direction of a uniform horizontal magnetic field of magnitude 0.80 T. What is the magnitude of torque experienced by the coil?
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 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 wire of size 2.5 cm × 4 cm carries a steady current of 1 A. A straight wire carrying 2 A current is kept near the loop as shown. If the loop and the wire are coplanar, find the (i) 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.
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).
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?
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`.
