Question

charge q in a spherical region of radius R changes with time t as q =2e^-3t the initial current density as the surface of a spherical reason is​

Answer 1

current density = 6/πR²

charge in q a spherical region of radius R changes with time t as q = 2e^{-3t}

we have to find initial current density of spherical region.

current density means current passing through per unit cross sectional area from the given region.

i.e., J = i/A

and current is the rate of change of charge with respect to time.

do, i = dq/dt = d(2e^{-3t})/dt = -6e^{-3t}

at t = 0, q = -6e^0 = -6 unit

hence, initial amount of current is 6.

now cross sectional of spherical region, A = πR²

[ note : total area of spherical region is 4πR² but cross sectional area is πR²]

so, current density , J = i/A = 6/πR²

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Answer 2

$\huge\bold\purple{Answer:-}$

charge in q a spherical region of radius R changes with time t as q = 2e^{-3t}

we have to find initial current density of spherical region.

current density means current passing through per unit cross sectional area from the given region.

i.e., J = i/A

and current is the rate of change of charge with respect to time.

do, i = dq/dt = d(2e^{-3t})/dt = -6e^{-3t}

at t = 0, q = -6e^0 = -6 unit

hence, initial amount of current is 6.

now cross sectional of spherical region, A = πR²