A ring of radius 5 cm is in ihc yz plane w ith its center at the orign. The ring

Question

A ring of radius 5 cm is in ihc yz plane w ith its center at the orign. The ring carries a uniform charge of 10 nC. Find the electric at x= 12cm. A proton starts at rest and is accclcratcd through a potential difference of 240 volts in the +x direction. It then enters a region of a Tesla uniform magnetic field in the plane of the page pointing toward the bottom of the page as shown. In what direction is the magnetic force felt bv the proton? B = The proton begins to move in a circular path perpendicular to the magnetic field lines. What is the radius of the circle? What must be the magnitude and direction of the uniform electric field needed in this region to ensure the proton moves in a straight line upon entering the region ?

Explanation / Answer

4.

Given that,

The radius of the ring is r=5 cm =0.05 m

the uniformly distributed charge is Q=10 nC = 10*10^-9 C =10^-8 C

in the yz plane the point at x=12 cm =0.12 m

by using pythagoras theorem,

r^2=(0.05 m)^2+(0.12 m)^2

r^2=0.0169 m^2=sqrt(0.0169 m^2)

r=0.13 m

electric potential is does not depends upon the direction and also all charge at same distance then

electric potential is written as,

V=kQ/r , Here k is the coulomb's constant its value is 9*10^9 N.m/C

Substitute all values in above expression,

V= (9*10^9 N.m/C * 10^-8 C)/(0.13 m)

=692 V

5.

a)

Towards the x direction

b)

the electric force is, F=qE=qV/d ==> Fd=qV

But the product of force and distance is the workdone then work done can be written as , W= Fd=1/2*m*v^2 then equate both equations,

we get,

1/2*m*v^2=q*V

rearranging the terms,

v=sqrt(2*q*V/m)

Bur we want radius of the circle then,

Circular force and magnetic forces are equate we get,

m*v^2/r=q*v*B then,

r=m*v/q*B

Substitute velocity in above expression then,

r=sqrt((2*V*m)/(q*B^2))

Here, 1.6*10^-27 kg for mass of the proton m, 1.6*10^-19 C for charge of proton q

Substitute the values in above expression,

we get,

r=sqrt((2*240 V*1.6*10^-27 kg)/(1.6*10^-19 C *(4.5 T)^2))

=6.8 m

c)

the electric field is also acting in x direction because electric and magnetic fields are perpendicular to each other.

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