Question

A Gaussian surface in the shape of a right circular cylinder with end caps has a radius of 10.3 cm and a length of 64.6 cm. Through one end there is an inward magnetic flux of 19.0 μWb. At the other end there is a uniform magnetic field of 2.18 mT, normal to the surface and directed outward. What are the (a) magnitude and (b) direction (inward or outward) of the net magnetic flux through the curved surface?

Answer 1

a)

₁= magnetic flux through first end = - 19 x 10^-6 Wb (negative sign for inward direction)

B = magnetic field through other end = 2.18 mT = 2.18 x 10^-3 T

r = radius of circular section = 10.3 cm = 0.103 m

A = area of other end = r² = (3.14) (0.103)² = 0.0333 m²

₂= magnetic flux through other end

magnetic flux through other end is given as

₂= B A = (2.18 x 10^-3) (0.0333) = 72.6 x 10^-6 Wb

₃ = magnetic flux through curved section

Since no net charge is enclosed by the gaussian surface, hence

₁+ ₂+ ₃ = 0

(- 19 x 10^-6) + (72.6 x 10^-6) + ₃ = 0

₃ = - 53.6 x 10^-6 Wb

magnitude : 53.6 x 10^-6 Wb

b)

direction :

the negative sign indicates inward direction.