A long solenoid of \(50~\text{cm}\) length having \(100\) turns carries a current of \(2.5~\text{A}\). The magnetic field at the centre of the solenoid is:
\(\big(\mu_0 = 4\pi\times 10^{-7}~\text{TmA}^{-1} \big)\)
1. \(3.4\times 10^{-4}~\text{T}\)
2. \(6.28\times 10^{-5}~\text{T}\)
3. \(3.14\times 10^{-5}~\text{T}\)
4. \(6.28\times 10^{-4}~\text{T}\)
A straight conductor carrying current \(I\) splits into two parts as shown in the figure. The radius of the circular loop is \(R\). The total magnetic field at the centre \(P\) of the loop is:
1. | zero | 2. | \(\dfrac{3\mu_0 i}{32R},~\text{inward}\) |
3. | \(\dfrac{3\mu_0 i}{32R},~\text{outward}\) | 4. | \(\dfrac{\mu_0 i}{2R},~\text{inward}\) |
Two toroids \(1\) and \(2\) have total no. of turns \(200\) and \(100\) respectively with average radii \(40~\text{cm}\) and \(20~\text{cm}\) respectively. If they carry the same current \(i\), what will be the ratio of the magnetic fields along the two loops?
1. \(1:1\)
2. \(4:1\)
3. \(2:1\)
4. \(1:2\)
A proton carrying \(1~\text{MeV}\) kinetic energy is moving in a circular path of radius \(R\) in a uniform magnetic field. What should be the energy of an \(\alpha \text- \)particle to describe a circle of the same radius in the same field?
1. \(1~\text{MeV}\)
2. \(0.5~\text{MeV}\)
3. \(4~\text{MeV}\)
4. \(2~\text{MeV}\)
1. | \({G \over (S+G)}\) | 2. | \({S^2 \over (S+G)}\) |
3. | \({SG \over (S+G)}\) | 4. | \({G^2 \over (S+G)}\) |
Charge q is uniformly spread on a thin ring of radius R. The ring rotates about its axis with a uniform frequency of f Hz. The magnitude of magnetic induction at the centre of the ring is:
1.
2.
3.
4.
A square loop, carrying a steady current I, is placed in a horizontal plane near a long straight conductor carrying a steady current I1 at a distance d from the conductor as shown in the figure. The loop will experience:
1. | a net attractive force towards the conductor |
2. | a net repulsive force away from the conductor |
3. | a net torque acting upward perpendicular to the horizontal plane |
4. | a net torque acting downward normal to the horizontal plane |
A current loop consists of two identical semicircular parts each of radius R, one lying in the x-y plane and the other in x-z plane. If the current in the loop is I, then the resultant magnetic field due to the two semicircular parts at their common centre is:
1.
2.
3.
4.