- 1(current)
Q. No.A metallic rod of \(1 ~\text m\) length is rotated with a frequency of \(50 ~\text{rev/s},\) with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius \(1 ~\text m,\) about an axis passing through the centre and perpendicular to the plane of the ring (as shown in the figure). A constant and uniform magnetic field of \(1 ~\text T\) parallel to the axis is present everywhere. What is the emf between the centre and the metallic ring?
1. \(150 ~\text V\)
2. \(130 ~\text V\)
3. \(157 ~\text V\)
4. \(133 ~\text V\)
A wheel with \(10\) metallic spokes each \(0.5~\text{m}\) long is rotated with a speed of \(120~\text{rev/min}\) in a plane normal to the horizontal component of Earth’s magnetic field \(H_E\) at a place. If \(H_E=0.4~\text{G}\) at the place, what is the induced emf between the axle and the rim of the wheel? (\((1~\text{G}=10^{-4}~\text{T})\)
1. \(5.12\times10^{-5}~\text{V}\)
2. \(0\)
3. \(3.33\times10^{-5}~\text{V}\)
4. \(6.28\times10^{-5}~\text{V}\)
Refer to figure. The arm \(PQ\) of the rectangular conductor is moved from \(x = 0,\) outwards. The uniform magnetic field is perpendicular to the plane and extends from \(x = 0\) to \(x = b\) and is zero for \(x > b.\) Only the arm \(PQ\) possesses substantial resistance \(r.\) Consider the situation when the arm \(PQ\) is pulled outwards from \(x = 0\) to \(x = 2b\) with a` constant speed \(v.\) The induced emf is:
| 1. | \(- Blv ~\text{for }~ 0 \leq x < b ,~~~ 0 ~\text{for}~ b \leq x < 2 b\) |
| 2. | \( + Blv ~\text{for}~ 0 \leq x < b , ~~~0 ~\text{for }~ b \leq x < 2 b\) |
| 3. | \(- Blv ~\text{for}~ b \leq x < 2 b , ~~~0 ~\text{for }~ 0 \leq x < b\) |
| 4. | \(+ Blv ~\text{for} ~ b \leq x < 2 b , ~~~ 0 ~\text{for}~ 0 \leq x < b\) |
Refer to the figure, the arm \(PQ\) of the rectangular conductor is moved from \(x=0,\) outwards. The uniform magnetic field is perpendicular to the plane and extends from \(x=0~to~x=b\) to \(x=b\) and is zero for \(x>b.\) Only the arm \(PQ\) possesses substantial resistance \(r.\) Consider the situation when the arm \(PQ\) is pulled outwards from \( x = 0 \) to \(x=2b\) with constant speed \(v.\) The force necessary to pull the arm is:
| 1. | \(~\dfrac{B^2l^2v}{r}~\text{for}~0\leq x<b,~0~\text{for}~b\leq x<2b\) |
| 2. | \(~\dfrac{B^2l^2v}{2r}~\text{for}~0\leq x<b,~0~\text{for}~b\leq x<2b\) |
| 3. | \(~0~\text{for}~0\leq x<b,~\dfrac{B^2l^2v}{r}~\text{for}~b\leq x<2b\) |
| 4. | \(~0~\text{for}~0\leq x<b,~\dfrac{B^2l^2v}{2r}~\text{for}~b\leq x<2b\) |
The arm \(PQ\) of the rectangular conductor is moved from \(x = 0,\) outwards. The uniform magnetic field is perpendicular to the plane and extends from \(x = 0\) to \(x = b\) and is zero for \(x > b.\) Only the arm \(PQ\) possesses substantial resistance \(r.\) Consider the situation when the arm \(PQ\) is pulled outwards from \(x = 0\) to \(x = 2b\) and is then moved back to \(x = 0\) with constant speed \(v.\) The power dissipated as Joule heat is:
| 1. | \(\dfrac{{B}^2 {l}^2 {v}}{2{r}}~~\text{for}~0 \leq {x}<{b},~~~ 0~~\text{for} ~{b} \leq {x}<2 {b}\) |
| 2. | \(\dfrac{{B}^2 {l}^2 {v^2}}{{r}}~~\text{for}~0 \leq {x}<{b},~~~ 0~~\text{for} ~{b} \leq {x}<2 {b}\) |
| 3. | \(0~~\text{for}~b \leq {x}<{2b},~~~ \dfrac{{B}^2 {l}^2 {v}^2}{{r}}~~\text{for} ~{0} \leq {x}< {b}\) |
| 4. | \(0~~\text{for}~b \leq {x}<{2b},~~~ \dfrac{{B}^2 {l}^2 {v}}{{2r}}~~\text{for} ~{0} \leq {x}< {b}\) |
Kamla peddles a stationary bicycle. The pedals of the bicycle are attached to a \(100\) turn coil of an area of \(0.10~\text{m}^2\). The coil rotates at half a revolution per second and it is placed in a uniform magnetic field of \(0.01~\text{T}\) perpendicular to the axis of rotation of the coil. What is the maximum voltage generated in the coil?
1. \(0.628~\text{V}\)
2. \(0.421~\text{V}\)
3. \(0.314~\text{V}\)
4. \(0\)
- 1(current)
Q. No.
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