Question

1. Two long solenoids are placed in the coaxial position, one inside the other, they have 30 cm and 20 cm diameters, respectively. The outer solenoid is 2 m long with 5000 turns, and carrying a current of 4 A. The inner one is 1 m long with 2000 turns, and carrying a current of 2 A in the opposite sense. Find the magnitude of the magnetic field (in mT) at any point on the solenoid axis inside.

A. 10.52
B. 3.68
C. 15.08
D. 7.54

2.

A straight conductor is split into identical semicircular turns, as shown in the figure. What is the magnetic field at the center of the circular loop?

  
A. μoi/2R
B. μoiR/4
C. 0
D. μoi/4R

3.

Which of the followings are correct for Ampere’s Law? (Choose three correct answers)

A. The magnetic field decreases non-linearly outside of a current carrying wire  
B. The net magnetic field is zero at the both end of the current carrying wire  
C. The magnetic field has its maximum value on the surface of a current carrying wire  
D. The magnetic field increases linearly within a current carrying wire from its center to its surface

Answer 1

1. Correct answer will be option c) 7.54

As per the given information we have,

They have 30 cm and 20 cm diameters, respectively.

The outer solenoid length l1 =2 m long

No of turns N1 = 5000 turns,

and current I1 = 4 A.

Lenght of inner one L2 = 1 m long

No of turns N2 = 2000

carrying a current I2 = 2 A in the opposite direction

Now for the magnitude of the magnetic field (in mT) at any point on the solenoid axis inside is given as,

Bin = u°(N1/L1 × I1 - N2/L2 × I2)

On plunging values we will get,

Bi = 4 × 3.14 × 10^-7 (5000/2 × 4 - 2000/1 ×2 )

Bin = 7.54 mT

Hence option c is correct here.

2. The correct answer will be option D) u°I /4R

Because,

Magnetic field at the centre of a semicircular loop will be = magnetic field at the centre of a circular loop/2 = U°I/2R × 1/2

Hence Bc  = u°i/4R

Hence option D is correct here.

3. Option A, C , D is correct here.

From the Ampere law we have the relation for the magnetic field of current carrying wire at different locations as,

Inside the wire of radius R and considered Amperes loop r as,

Bin = U°Ir/2 pie R^2

Form here we can see that  The magnetic field has its maximum value on the surface of a current carrying wire hence option C is correct,

Also form here we can see that,

The magnetic field increases linearly within a current carrying wire from its center to its surface

Hence option D is also correct.

Now magnetic field outside the wire will be of radius r'

Bo = U°I/2 pie r'

Here we can say that magnetic field is inversely proportional to the distance so here it has non linear distribution so option A is also correct here.

Hence option A C and D is correct here

For option B as the magnetic field is present on both the ends also so they will not be zero at ends hence option B is incorrect here.