Question

A uniform but time variable magnetic field of induction B=a+bt fills a cylindrical region of radius R .A conducting rod PQ of length 2R is pivoted at P situated at a horizontal distance sqrt(3)R from the centre of the magnetic field as shown.At t=0 the rod starts rotating clockwise with constant angular velocity omega .Find the emf induced in the rod at the instant end Q of the rod enters the magnetic field.​

Answer 1

Answer:

Explanation:

A uniform magnetic field of induction B fills a cylindrical volume of radius R. A rod AB of length 2l is placed as shown in figure. If B is changing at the rate dB/dt, the emf that is produced by the changing magnetic field and that acts between the ends of the rod is

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November 22, 2019avatar

Taher Waran

ANSWER

Emf induced between the ends of the rod E=A.  

dt

dB

​  

 

where A is the area of the triangular AOB

From figure, OC=  

OB  

2

−BC  

2

 

​  

 

∴ OC=  

R  

2

−l  

2

 

​  

 

Area of the triangle A=  

2

1

​  

×OC×AB  

∴ A=  

2

1

​  

 

R  

2

−l  

2

 

​  

(2l)=l  

R  

2

−l  

2

 

​  

 

⟹ Emf induced between the ends of the rod E=  

dt

dB

​  

l  

R  

2

−l  

2

 

​