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 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.
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.
Figure shows a conducting circular loop of radius a placed in a uniform, perpendicular magnetic field B. A thick metal rod OA is pivoted at the centre O. The other end of the rod touches the loop at A. The centre O and a fixed point C on the loop are connected by a wire OC of resistance R. A force is applied at the middle point of the rod OAperpendicularly, so that the rod rotates clockwise at a uniform angular velocity ω. Find the force.
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 ______.
