Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Plane of the loop is at an angle with the direction of the magnetic field,
Let the angle between the field and the normal is θ. The forces on BC and DA are equal and opposite and they cancel each other as they are collinear.
Force on AB is F1 and force on CD is F2, thus
F1 = F2 = IbB
Magnitude of torque on the loop as in the figure:
`because tau =F_1 1/2 sintheta +F_2 1/2 sintheta =IlBsintheta`
or, τ = IAB sin θ (Where area,A = lb)
If there are ‘n’ such turns the torque will be nIAB sinθ
Magnetic moment of the current, m = IA
`vectau=vecm xx vecB`
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 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.
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.
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?
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.
