Difficult Questions

## Electromagnetic Induction

- Are you well prepared? Practice hard questions to be more confident about the chapter
1
Varying electric current produces magnetic field due to which emf is induced in a closed loop placed near to the current carrying conductor. Let's solve a problem to understand how it works.
A long straight wire is parallel to one edge as in fig. If the current in the long wire is varies in time as  what will be the induced emf in the loop?
A
B
C
D
2
Faraday's Law says that the emf induced (and therefore the current induced) in the loop is proportional to the rate of change in magnetic flux. Calculate induced emf in a coil caused by varying flux due to magnetic field.
A rectangular loop of length and breadth is placed at a distance of from an infinitely long wire carrying current such that the direction of current is parallel to breadth. If the loop moves away from the current wire in a direction perpendicular to it with a velocity , the magnitude of the e.m.f. in the loop is ( permeability of free space)
A
B
C
D
3
There are three ways to change the magnetic flux through a loop:
• Change the magnetic field strength (increase, decrease) over the surface area.

• Change the area of the loop (increase by expanding the loop, decrease by shrinking the loop).

• Change the angle between the surface defined by the loop and the magnetic field vector. Remember that flux is the integral of the dot product between and .

Solve problems where circuit is rotating in the plane of magnetic field.
Two identical cycle wheels (geometrically) have different number of spokes connected from center to rim. One is having spokes and the other having only (the rim and the spokes are resistanceless). One resistance of value is connected between center and rim. The current in will be
A
double in the first wheel than in the second wheel
B
four times in the first wheel than in the second wheel
C
will be double in the second wheel than that of the first wheel
D
will be equal in both these wheels
E
4
A current carrying coil is placed in a magnetic field and when it is altered (rotated) from its initial position, magnetic induction takes place. this is all based on Faraday's law of induction and Lenz's law. Let's solve a problem.

A coil of 50 turns and area  is pivoted about a vertical diameter in a uniform current of the horizontal magnetic field and carries a current of 2A. When the coil is held with its plane in N-S direction, it experiences a couple of 0.04 N-m; and when its plane is E-W, the corresponding couple is 0.03 N-m. The magnetic induction is

A
0.2 T
B
0.3 T
C
0.4 T
D
0.5 T
5
When a metallic closed loop pattern of wire is placed in a varying magnetic field, emf is induced inside the loop.
Let's solve a problem by considering the resistance of wire and understand how it works.
A triangular wire (each side =2m)is placed in are region of time magnetic field having . The magnetic field is perpendicular to the plane of the triangle . The base of the triangle AB has a resistance while the other two sides have resistance each . The magnitude of potential difference between the points A and B will be
A
0.4 V
B
0.6 V
C
1.2 V
D
None
6
An emf induced by motion relative to a magnetic field B is called a motional emf. Let see how this concept is used to move a rod in a constant magnetic field and also the charging of a capacitor with the passes of time.
When the acceleration of rod is zero, the charge on capacitor is :

A
B
C
D
7
A thin insulated wire forms a plane spiral of N tight turns carrying a current I due to which magnetic induction produced at the centre of the spiral. It works on the principle of Biot-Savart's law.
A thin insulated wire forms a plane spiral of tight turns carrying a current . The radii of inside and outside turns (Fig.) are equal to and Find:
(a) the magnetic induction at the centre of the spiral;
(b) the magnetic moment of the spiral with a given current.
8
In many house hold electrical appliances we have electrical circuits involving multiple resistors and inductors, these circuits are called LR circuits or inductor circuits. Solve a problem on LR circuits for better understanding.
The maximum charge on the capacitor
A
B
C
D