Advertisements
Advertisements
प्रश्न
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?
उत्तर
Magnetic field strength, B = 3000 G = 3000 × 10−4 T = 0.3 T
Length of the rectangular loop, l = 10 cm
Width of the rectangular loop, b = 5 cm
Area of the loop,
A = l × b = 10 × 5 = 50 cm2 = 50 × 10−4 m2
Current in the loop, I = 12 A
Now, taking the anti-clockwise direction of the current as positive and vice-versa:
(a) Torque, `vecτ = "I"vec"A" xx vec"B"`
From the given figure, it can be observed that A is normal to the y–z plane and B is directed along the z-axis.
∴ τ = `12 xx (50 xx 10^-4)hat"i" xx 0.3 hat"k"`
= `-1.8 xx 10^-2 hat"j" "N m"`
The torque is 1.8 × 10−2 N m along the negative y-direction. The force on the loop is zero because the angle between A and B is zero.
(b) This case is similar to case (a). Hence, the answer is the same as (a).
(c) Torque, `τ = "I"vec"A" xx vec"B"`
From the given figure, it can be observed that A is normal to the x–z plane and B is directed along the z-axis.
∴ τ = `-12 xx (50 xx 10^-4)hat"j" xx 0.3 hat"k"`
= `-1.8 xx 10^-2 hat"i" "N m"`
The torque is 1.8 × 10−2 N m along the negative x-direction and the force is zero.
(d) Magnitude of torque is given as:
|τ| = IAB
= 12 × 50 × 10−4 × 0.3
= 1.8 × 10−2 N m
Torque is 1.8 × 10−2 N m at an angle of 240° with positive x-direction. The force is zero.
(e) Torque, `τ = "I"vec"A" xx vec"B"`
= `(50 xx 10^-4 xx 12) hat"k" xx 0.3 hat"k"`
= 0
Hence, the torque is zero. The force is also zero.
(f) Torque, `τ = "I"vec"A" xx vec"B"`
= `(50 xx 10^-4 xx 12) hat"k" xx 0.3 hat"k"`
= 0
Hence, the torque is zero. The force is also zero.
In case (e), the direction of `"I"vec"A"` and `vec"B"` is the same and the angle between them is zero. If displaced, they come back to an equilibrium. Hence, its equilibrium is stable.
Whereas, in case (f), the direction of `"I"vec"A"` and `vec"B"` is opposite. The angle between them is 180°. If disturbed, it does not come back to its original position. Hence, its equilibrium is unstable.
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?
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.
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.
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 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?
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 ______.
