Question

In the figure below, a uniform electric field is directed out of the page within a circular region of radius R = 2.50 cm. The magnitude of the electric field is given by E = (5.40 × 10 3 V/m . s t where t is in seconds. (a) What is the magnitude of the induced magnetic field at a radial distance of 2.00 cmi? (b) What is it at a radial distance of 5.00 cm?

Answer 1

Given that electric field is given by E =(5.40*10^-3 V/m•s)t

Radius of the circular region R = 2.50 cm = 0.025m

Then know that

6B.ds аф Е μοεο-dt =

a ) Now for r < R   B(2pir ) =μ₀ε₀AdE/dt

               B(2πr)=  μ₀ε₀*pir²*dE/dt

dE/dt = 5.40 * 10^-3 V/ms

Then   B =[(μ₀ε₀*r)dE/dt]/2

μ₀ =4pi*10^-7 H/m

ε₀ = 8.85 * 10^-12 C2/Nm²

r = 2.0 cm = 0.02 m

B = (4pi*10^-7 H/m)*(8.85 * 10^-12 C2/Nm²)*0.02 m *5.40 *10^-3 V/ms/2   =6.00 *10^-22 T Answer

b) for r > R  

Then   B(2πr )=  μ₀ε₀*πR²*dE/dt

B =μ₀ε₀*R²*dE/dt /2r

Here r = 5.0 cm = 0.05 m

Then B=  (4pi*10^-7H/m)*(8.85 *10^-12 ^C2/Nm²)*((0.025)^2 m2) *5.40*10^-23 V/ms/2*0.05m  

= 3.75* 10^-22 T Answer

I hope help you !!