NTA Abhyas JEE Main2020PhysicsMagnetic Effects of CurrentPractice
A cylindrical conductor of radius R carrying current i along the axis such that the magnetic field inside the conductor varies as B = B 0 r 2 0 < r ≤ R , then which of the following is incorrect ?
Options
- ACurrent density at distance ‘ r ’ from central axis of the conductor is J ( r ) = 2 B 0 r μ 0
- BCurrent density at distance ‘ r ’ from central axis of the conductor is J ( r ) = 3 B 0 r μ 0
- CHalf of the total current would be confined within the radius of R 2 1 3 of the conductor
- DFor r > R magnetic field would vary as B ( r ) = B 0 R 3 r
Correct answer
A. Current density at distance ‘ r ’ from central axis of the conductor is J ( r ) = 2 B 0 r μ 0
Step-by-step solution
Hint: Use Ampere’s law Sol: As B r = B 0 r 2 ∴   Total current (upto R ) B 0 R 2 2 π R = μ 0 I 0   ⇒   I 0 = 2 π R 3 B 0 μ 0 And let upto 'r' it confines half of the current. Then B 0 r ' 2 · 2 π r ' = μ 0 I 0 2 ⇒   B 0 · 2 π r ' 3 = μ 0 2 · 2 π R 3 B 0 μ 0 ⇒   r ' = R 2 1 3 Now let J → ( r ) is the current density at ‘ r ’ Then B 0 r 2 · 2 π r = μ 0 ∫