For the following statements, indicate whether the statement is true or false and explain in words your reasoning.

a) if i increase the number of moving charged particles per cubic meter in a conductor, i will have to increase the cross sectional area of the conductor to get the same amount of current for the same electric field in the conductor.

b) the change in magnetic flux in a closed loop induces an emf that opposes the change in magnetic flux.

c) the magnetic force per unit length of two long, parallel, current-carrying conductors is repulsive if the currents are flowing in the opposite direction.

d) . the total magnetic flux through a closed surface is equal to μ0i enclosed

make sure to explain your reasoning

a) If I increase the number of moving charged particles per cubic meter in a conductor, I will have to increase the cross sectional area of the conductor to get the same amount of current for the same electric field in the conductor.

FALSE

As we know that

so here if we increase the number of charge per unit volume then we need to decrease the area to get same amount of current through the wire.

b) The change in magnetic flux in a closed loop induces an EMF that opposes the change in magnetic flux.

TRUE

As per lenz law the direction of induced EMF is always opposite to the change in the flux due to which EMF is induced in the closed loop.

c) The magnetic force per unit length of two long, parallel, current-carrying conductors is repulsive if the currents are flowing in the opposite direction.

TRUE

When magnetic field of first wire will interact with other then it will exert force on it

so here the force will be on other wire such that the two wire will repel when current in the two wires is opposite in direction.

d) . The total magnetic flux through a closed surface is equal to μ0I enclosed

FALSE

magnetic flux is the number of field lines passing through a given area

So it is given as

newton's first law of motion

probably not if net force is zero