Two imaginary spherical surfaces of radius R and 2R respectively surround a positive point charge Q located at the center of the concentric spheres. When compared to the number of field lines N1 going through the sphere of radius R, the number of electric field lines N2 going through the sphere of radius 2R is

N2 = ¼N1

Explanation:

First of all, let's define the terms;

N1 = number of electric field lines going through the sphere of radius R

N2 = number of electric field lines going through the sphere of radius 2R

Q = the charge enclosed at the centre of concentric spheres

ε_o = a constant known as "permittivity of the free space"

E1 = Electric field in the sphere of radius R.

E2 = Electric field in the sphere of radius 2R.

A1 = Area of sphere of radius R.

A2 = Area of sphere of radius 2R

Now, from Gauss's law, the electric flux through the sphere of radius R is given by;

Φ = Q/ε_o

We also know that;

Φ = EA

Thus;

E1 × A1 = Q/ε_o

E1 = Q/(ε_o × A1)

Where A1 = 4πR²

E1 = Q/(ε_o × 4πR²)

Similarly, for the sphere of radius 2R,we have;

E2 = Q/(ε_o × 4π(2R)²)

Factorizing out to get;

E2 = ¼Q/(ε_o × 4πR²)

Comparing E2 with E1, we arrive at;

E2 = ¼E1

Now, due to the number of lines is proportional to the electric field in the each spheres, we can now write;

N2 = ¼N1

elly's long hair:

a. if the salon only takes cash, then this isn't the problem. it doesn't matter how much she has in her checking account.   she can't get a haircut until she has the cash.

b. if she has overdraft protection, then there's no problem.   she can go ahead and write a check that her account can't cover, then sometime later, pay the bank some outrageous usury for loaning her a few bucks for a few days, but with beautiful hair.

c. if elly has some principles, and doesn't want to write a bad check, then now she has a problem.   her desire for the new hairstyle is in conflict with her honesty and integrity.

d.   if the bank will not process a check she writes, then even if she had a million $$ in her account, she couldn't use any of it.   the amount she has in her account is not the problem.   and if i may suggest, she might as well close her checking account, and put the money where it'll work for her.   it's not doing her a bit of good in a checking account, since she can't write any checks.

justin can't pay the full balance:

a. he can't even handle the credit limit he has now.   under no circumstances should he ask for a higher limit.

b.   he can ask for the grace period to be extended.   but that's no solution, the bank will almost certainly refuse anyway, and there are much better options.   he knew the rules of his credit card when he started using it.

c.   he definitely should pay the interest on the balance, plus as much of the balance as he can cover at the same time.

d.   he definitely should pay the minimum otherwise they could shut down his card.   he should also pay as much more as he possibly can.   he should also remember the awkward situation he's in, stop buying stuff on credit that he can't afford, and avoid adding any more debt.

i'd say that justin's best best option isn't on this list of choices.   what he has to do:   pay as much as he can at least the minimum payment plus as much more as he can and then avoid adding more debt.

unlike poles attract