Dependence on Area and Orientation

Q. A hypothetical butterfly net is in a uniform electric field of magnitude $E=3.0\hat{i}{\text{mNC}}^{-1}$. The circular rim of radius $R=11\text{cm}$, is aligned perpendicular to the field as shown in the diagram. If the butterfly net contains no net charge then find the magnitude of electric flux $(|\varphi |)$ passing through the circular rim of net.

1. $1.114\times {10}^{-4}{\text{Nm}}^2{\text{C}}^{-1}$
2. $3.342\times {10}^{-4}{\text{Nm}}^2{\text{C}}^{-1}$
3. $0{\text{Nm}}^2{\text{C}}^{-1}$
4. $2.228\times {10}^{-4}{\text{Nm}}^2{\text{C}}^{-1}$

Q. A flat coil of $500$ turns, each of area $50c{m}^2$, rotates in a uniform magnetic field of $0.1Wb/m^2$ about an axis normal to the field at an angular speed of $150rad/s$. (Initially magnetic field was along the area vector of the field). The coil has a resistance of $15\Omega$. Maximum induced current in the coil is

1. $1.5A$
2. $2.5A$
3. $3.5A$
4. $4.5A$

Q. The figure shows a conducting ring of radius $R$. A uniform steady magnetic field $B$ lies perpendicular to the plane of the ring in a circular region of radius $r(<R)$. If the resistance per unit length of the ring is $\lambda$, then the current induced in the ring when its radius gets doubled is

1. $\frac{BR}{\lambda }$
2. $\frac{2BR}{\lambda }$
3. $\text{Zero}$
4. $\frac{B{r}^2}{4R\lambda }$

Q.

A coil of area $80$$c{m}^2$ and 50 turns is rotating with 2000 revolutions per minute about an axis perpendicular to a magnetic field of $0.05$ $Tesla$. The maximum value of the e.m.f. induced in it is

1. 

2. 

3. 

4. 

Q. A wire loop is rotated in a magnetic field. The frequency of change of direction of the induced emf is

1. Twice per revolution
2. Four times per revolution
3. Six times per revolution
4. Once per revolution

Q. The magnetic flux $\left(\varphi \right)$ through a coil varies with time $t$ as shown in the diagram. Which graph best represents the variation of the e.m.f $E$ induced in the coil with time $t$ ?

1. 
2. 
3. 
4. 

Q. A wire in the form of a circular loop of radius $r$ lies with its plane normal to a magnetic field $B$. If the wire is pulled to take a square shape in the same plane in time $t$, the emf induced in the loop is given by

1. $\frac{\pi B{r}^2}{t}(1-\frac{\pi }{10})$
2. $\frac{\pi B{r}^2}{t}(1-\frac{\pi }{8})$
3. $\frac{\pi B{r}^2}{t}(1-\frac{\pi }{6})$
4. $\frac{\pi B{r}^2}{t}(1-\frac{\pi }{4})$

Q. A wire $40cm$ long is bent into a rectangular frame $15cm\times 5cm$ and placed perpendicular in a magnetic field intensity of $0.8T$ . The frame is changed into a square frame and the field is increased to $1.4T$ in a time interval of $0.5s$. The e.m.f induced in the frame is ________.

1. $1.6\times {10}^{-2}V$
2. $1.6\times {10}^{-3}V$
3. $1.6\times {10}^{-4}V$
4. $1.6\times {10}^{-5}V$

Q. A wire $40cm$ long is bent into a rectangular frame $15cm\times 5cm$ and placed perpendicular in a magnetic field intensity of $0.8T$ . The frame is changed into a square frame and the field is increased to $1.4T$ in a time interval of $0.5s$. The e.m.f induced in the frame is ________.

1. $1.6\times {10}^{-2}V$
2. $1.6\times {10}^{-3}V$
3. $1.6\times {10}^{-4}V$
4. $1.6\times {10}^{-5}V$

Q.

A coil of area $80$$c{m}^2$ and 50 turns is rotating with 2000 revolutions per minute about an axis perpendicular to a magnetic field of $0.05$ $Tesla$. The maximum value of the e.m.f. induced in it is

1. 

2. 

3. 

4. 

Q. The figure shows a conducting ring of radius $R$. A uniform steady magnetic field $B$ lies perpendicular to the plane of the ring in a circular region of radius $r(<R)$. If the resistance per unit length of the ring is $\lambda$, then the current induced in the ring when its radius gets doubled is

1. $\frac{BR}{\lambda }$
2. $\frac{2BR}{\lambda }$
3. $\text{Zero}$
4. $\frac{B{r}^2}{4R\lambda }$

Q. A wire loop is rotated in a magnetic field. The frequency of change of direction of the induced e.m.f. is -

1. Four times per revolution
2. Twice per revolution
3. Once per revolution
4. Six times per revolution