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CBSE Class 12-science Answered

How much energy is stored in a 3 cm diameter, 12 cm long solenoid that has 200 turns of wire and carries a current of 0.8A?

Asked by arjunsah797 | 26 Mar, 2022, 09:10: AM
Expert Answer
Energy U stored per unit volume in magnetic field  is given as
 
U = (1/2) ( B2 / μo )....................... (1)
 
where B is magnetic field induction and μo is permeability of free space
 
Magnetic field induction B in solenoid is given as
 
B = μo ( N / L ) I ..............................(2)
 
where N is number of turns, L is length of solenoid and I is current passing through solenoid
 
Using eqn.(2) , we get energy U stored per unit volume from eqn.(1) as
 
U = (1/2) μo ( N / L )2 I2
 
Energy E stored in solenoid is obtained by multiplying above expression by volume ( A × L ) of solenoid ,
where A is crosssection area of solenoid .
 
E = [ (1/2) μo ( N / L )2 I2 ] × ( A × L )  
 
begin mathsize 14px style E space equals space mu subscript o over 2 cross times fraction numerator A space N squared space I squared over denominator L end fraction end style
By substituting values in above expression , we get E = 9.5 × 10-5 J

Answered by Thiyagarajan K | 26 Mar, 2022, 12:11: PM
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