A proton travels through uniform magnetic and electric fields. The magnetic field is in the negative x direction and has a magnitude of 2.85 mT. At one instant the velocity of the proton is in the positive y direction and has a magnitude of 2840 m/s. At that instant, what is the magnitude of the net force acting on the proton if the electric field is (a) in the positive z direction and has a magnitude of 5.38 V/m, (b) in the negative z direction and has a magnitude of 5.38 V/m, and (c) in the positive x direction and has a magnitude of 5.38 V/m

Explanation:

a ) Magnetic force on proton

= B q v , B is magnetic field , q is charge with velocity v

= 2.85 x 10⁻³ x 1.6 x 10⁻¹⁹ x 2840

= 12.95 x 10⁻¹⁹ N

Its direction will be towards positive z - direction according to Fleming's left hand rule.

force on proton due to electric field = charge x electric field.

= 1.6 x 10⁻¹⁹ x 5.38

= 8.608 x 10⁻¹⁹ N

this force will be along the field ie in positive z direction so both the forces are acting in the same direction so they will add up.

total force =  (12.95 + 8.608)x 10⁻¹⁹

= 21.558 x 10⁻¹⁹ N .

b ) in this case , both the forces are acting in opposite direction . net force

=  (12.95 - 8.608)x 10⁻¹⁹

= 4.342 x 10⁻¹⁹ N

c ) In this case both the forces are acting perpendicular to each other

resultant = √(12.95² + 8.608²) x 10⁻¹⁹ N

= 15.54 x 10⁻¹⁹ N .

answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases . this process does not change the mass number.

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as -decay. in this the mass number remains same.

from the above information, we see that only alpha-decay is producing a change in the mass number of the nucleus.

fgravity=10x10=100n case 1

fgravity=30x20=600n case 2

6 times more