Torque

Q. The electric force on a charge $q_1$ due to $q_2$ is $(4\hat{i}-3\hat{j})\text{N}$. The unit vector in the direction of electirc force on $q_2$ due to $q_1$ will be:

1. $-\frac{4}{5}\hat{i}-\frac{3}{5}\hat{j}$
2. $\frac{4}{5}\hat{i}+\frac{3}{5}\hat{j}$
3. $\frac{-4}{5}\hat{i}+\frac{3}{5}\hat{j}$
4. $-4\hat{i}+3\hat{j}$

Q. Two infinitely long static line charge of constant positive line charge density $\lambda$ are kept parallel to each other. If a point charge $+q$ is kept in equilibrium between them and is given small displacement along $x-$ axis about its equilibrium position then the correct statement is
[Charge $+q$ is confined to move in the $x$ direction only]

1. Charge takes circular path
2. Charge takes parabolic path
3. Charge contines to move in the direction of its displacement
4. Charge executes simple harmonic motion

Q. A circular coil of diameter 10 cm has 10 turns and carries a current of 5A. It is placed in a uniform field of 0.5 T with its plane parallel to the field. The torque on the coil in Nm, is

1. $\left(6.25\pi \right)\times {10}^{-2}$ N-m
   
2. $\left(6.25\pi \right)\times {10}^{-3}$ N-m
3. $\left(6.25\pi \right)\times {10}^{-4}$ N-m
4. Zero

Q. A molecule with dipole moment $p$ is placed in an electric field of strength $E$. Initially the dipole is aligned parallel to the field . If the dipole is to be rotated to be anti-parallel to the field , the work required to be done by an external agency is

1. $-2pE$
2. $2pE$
3. $pE$
4. $-2pE$

Q. What should be the orientation of an electric dipole in a uniform electric field, that corresponds to stable equilibrium ?

1. $\theta ={90}^{\circ }$
2. $\theta ={30}^{\circ }$
3. $\theta =0^{\circ }$
4. $\theta ={180}^{\circ }$

Q. If ${\theta }_1$ and ${\theta }_2$ be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip $\theta$ is given

1. ${\tan }^2\theta ={\tan }^2{\theta }_1-{\tan }^2{\theta }_2$
2. ${\cot }^2\theta ={\cot }^2{\theta }_1+{\cot }^2{\theta }_2$
3. ${\tan }^2\theta ={\tan }^2{\theta }_1+{\tan }^2{\theta }_2$
4. ${\cot }^2\theta ={\cot }^2{\theta }_1-{\cot }^2{\theta }_2$

Q. If ${\theta }_1$ and ${\theta }_2$ be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip $\theta$ is given

1. ${\tan }^2\theta ={\tan }^2{\theta }_1-{\tan }^2{\theta }_2$
2. ${\cot }^2\theta ={\cot }^2{\theta }_1+{\cot }^2{\theta }_2$
3. ${\tan }^2\theta ={\tan }^2{\theta }_1+{\tan }^2{\theta }_2$
4. ${\cot }^2\theta ={\cot }^2{\theta }_1-{\cot }^2{\theta }_2$

Q. Four wires each of length 2.0 metres are bent into four loops P, Q, R and S and then suspended into uniform magnetic field. Same current is passed in each loop. Which statement is correct?

1. Couple on loop P will be the highest
2. Couple on loop Q will be the highest
3. Couple on loop R will be the highest
4. Couple on loop S will be the highest

Q. An equilateral triangular loop of side l carries a current I. It is placed in a magnetic field B such that the plane of the loop is in the direction of B. The torque on the loop is

1. Zero
2. IBl
3. $\frac{\sqrt{3}}{2}I{l}^2{B}^2$
4. $\frac{\sqrt{3}}{4}IB{l}^2$

Q. A wire of length L is bent in the form of a circular coil and current i is passed through it. If this coil is placed in a magnetic field then the torque acting on the coil will be maximum when the number of turns is

1. As large as possible
2. Any number
3. 2
4. 1

Q. An electric field of $1000\text{V/m}$, is applied to an electric dipole moment of ${10}^{-29}C\cdot m.$ What is the potential energy of the electric dipole?

1. $-10\times {10}^{-29}J$
2. $-7\times {10}^{-27}J$
3. $-9\times {10}^{-20}J$
4. $-20\times {10}^{-18}J$

Q. A rectangular coil 6 cm long and 2 cm wide is placed in a magnetic field of 0.02 T. If the loop contains 200 turns and carries a current of 50 mA, the torque on the coil when its area vector is perpendicular to the field will be?

1. $2.4\times {10}^{-4}Nm$
2. 2.4 Nm
3. 0.24 Nm
4. 0.024 Nm

Q. A circular loop of area $1c{m}^2$, carrying a current of 10 A, is placed in a magnetic field of 0.1 T perpendicular to the plane of the loop. The torque on the loop due to the magnetic field is

1. $Zero$
2. ${10}^{-4}N-m$
   
3. ${10}^{-2}N-m$
4. $1N-m$

Q. A coil carries a current and experiences a torque due to a magnetic filed. The value of the torque is 80% of the maximum possible torque. The angle between the magnetic field and the normal to the plane of the coil is

1. ${30}^{\circ }$
2. ${53}^{\circ }$
3. ${45}^{\circ }$
4. ${37}^{\circ }$

Q. An equilateral triangular loop of side l carries a current I. It is placed in a magnetic field B such that the plane of the loop is in the direction of B. The torque on the loop is

1. Zero
2. IBl
3. $\frac{\sqrt{3}}{2}I{l}^2{B}^2$
4. $\frac{\sqrt{3}}{4}IB{l}^2$